Addressing the Collective Action Dilemma in Resident-Led Urban Regeneration: Designing and Verifying a Multi-Dimensional Policy Lever System Through Evolutionary Game Theory

Abstract

Against the backdrop of urban stock development worldwide, resident-led urban regeneration and in-situ demolition-and-reconstruction models are crucial for advancing sustainable urban regeneration. However, these initiatives often stall due to collective action dilemmas arising from complex interactions among governments, residents, and contractors. To address this, we develop a tripartite evolutionary game model that incorporates a novel multi-dimensional policy lever system. This system integrates the following: (1) resource-allocation levers (area-expansion coefficient, w; expansion benefit-sharing coefficient, v), (2) cost-sharing levers (expansion-purchase coefficient, p; original-area reconstruction payment coefficient, q), and (3) behavioral-intervention levers (cost-burden perception coefficient, e; accident-risk perception coefficient, d), the latter quantifying behavioral economics principles like loss aversion and probability weighting. Through numerical simulations, we identify the nonlinear effects, critical thresholds, and interaction mechanisms of these levers. The results demonstrate that resource-allocation and cost-sharing levers exhibit critical ranges, whereas behavioral-intervention levers are characterized by perception thresholds and saturation effects. Crucially, coordinated optimization of all parameters—rather than one-sided incentives—is essential to steer the system towards the ideal cooperative equilibrium (government guidance, contractor participation, and resident engagement). This study provides a systematic theoretical framework and practical pathway for crafting targeted urban regeneration policies, emphasizing that aligning economic incentives with behavioral interventions can simultaneously enhance compactness, feasibility, and equity, thereby contributing to the achievement of Sustainable Development Goal 11.

1. Introduction

Urban regeneration has emerged as a global agenda for addressing urban shrinkage, spatial decline, and social transformation [1,2]. Internationally, the paradigm of urban regeneration has undergone a profound shift from government-led, large-scale physical redevelopment (Top-down Redevelopment) to approaches that emphasize multi-stakeholder collaboration, community empowerment, and cultural continuity—namely Co-production and Participatory Revitalization [3,4,5]. The core of this transition lies in recognizing that urban space is not merely an aggregation of physical assets but a locus of social relations and community identity. Consequently, involving diverse actors—residents, non-governmental organizations (NGOs), and others is regarded as pivotal to achieving more inclusive and sustainable regeneration, a proposition that has demonstrated remarkable vitality in high-density East Asian urban contexts [6,7,8]. Among these practices, in-situ demolition-and-reconstruction, which replaces original structures by rebuilding on the same parcel, seeks to fundamentally improve residents’ living conditions and asset values while preserving existing social capital and neighborhood structure, thereby offering a promising pathway toward sustainable urban regeneration [9,10,11].

China is confronting the pressing reality of a vast stock of aging residential compounds urgently in need of renewal, making the transformation of urban renewal models imperative [12,13,14]. In recent years, policies from the central to local levels have encouraged the participation of private capital and the co-construction, co-governance, and shared benefits of residents [12,15,16,17,18,19]. Represented by community regeneration pilots such as “Zhegong Xincun” in Zhejiang Province, a wave of resident-led urban regeneration practices characterized by in-situ demolition-and-reconstruction has emerged. Here, ‘resident-led renewal’ refers to a governance model where residents act as the primary decision-makers and investors, whereas ‘in-situ demolition-and-reconstruction’ is a specific physical approach within this model, involving rebuilding on the original parcel. Through benefit-sharing mechanisms, these pilots have successfully activated resident investment, contractor participation, and government guidance, gradually shaping localized solutions with national demonstration significance [14,20,21]. This study is situated against the pressing national backdrop outlined in China’s ‘Guiding Opinions on Comprehensively Advancing the Renovation of Old Urban Residential Communities,’ which targets the renovation of approximately 215,000 aging urban residential communities (involving nearly 50 million households) by the end of 2025 [15]. Scaling and replication call for context-sensitive decision-making indicator systems and the design of coordination mechanisms to enhance both sustainable governance performance and scalability [22].

Nevertheless, promoting this model is far from straightforward; its success hinges on the complex and dynamic strategic interactions among the three core stakeholders—government, residents, and contractors. All parties exhibit pronounced features of bounded rationality, with behavior jointly shaped by risk perception, expected returns, and evolutionary learning [19,23]. Governments must balance social benefits, fiscal outlays, and political risks, crafting differentiated mixes of incentives and regulation [12,19]. Residents, while able to anticipate long-term gains, are highly sensitive to short-term contribution costs, and their decisions are strongly influenced by subjective perceptions and neighborhood trust [23,24]. Contractors weigh current profits, market share, and long-term reputation, with strategic choices jointly driven by policy incentives and market expectations [25,26]. Such complexity frequently gives rise to collective action dilemmas, pushing projects into a “hot government—active market—cold residents” stalemate, which in turn, constitutes the critical bottleneck determining whether resident-led urban regeneration can progress from isolated successes to broad, scalable adoption [12,14,24,27].

Despite valuable explorations of resident-led urban regeneration through case analyses and policy reviews—and preliminary attention to various incentive instruments—the scholarly literature exhibits two critical limitations. First, most studies examine a single class of policy instrument in isolation (e.g., floor area ratio (FAR) bonuses or fiscal subsidies), lacking an integrated policy-portfolio perspective that encompasses the triad of resource allocation, cost sharing, and behavioral intervention, thereby obscuring potential synergistic effects among instruments [28,29,30]. Second, a substantial body of analyses (including some game-theoretic studies) remains predicated on the fully rational homo economicus assumption, underestimating the pivotal role of cognitive biases in residents’ decision-making (e.g., loss aversion and nonlinear probability weighting). As a result, policy design often lacks a robust micro-level psychological-behavioral foundation and thus fails to effectively overcome bottlenecks to resident participation [31,32,33,34].

To address the foregoing gaps, this paper proposes and embeds a tripartite evolutionary game framework grounded in a multi-dimensional policy-lever system to systematically characterize the strategy evolution and stability properties of governments, residents, and contractors in resident-led urban regeneration. The system comprises three classes of operational policy levers:

• Resource-allocation levers (the area-expansion coefficient (w) and the expansion benefit-sharing coefficient (v)), which regulate value creation and distribution structures;
• Cost-sharing levers (the expansion-purchase coefficient (p) and the original-area reconstruction payment coefficient (q)), which refine the allocation of contribution burdens;
• Behavioral-intervention levers (the cost-burden perception coefficient (e) and the accident-risk perception coefficient (d)), which quantify and model principles from behavioral economics (e.g., loss aversion and risk perception) to capture and correct residents’ cognitive biases.

Through this integrative framework, we dynamically simulate the evolutionary trajectories of the three parties’ strategies and, in particular, elucidate the threshold effects and interaction mechanisms of the various policy levers.

Building on this framework, this paper aims to systematically address three core research questions:

• Under a bounded-rationality setting involving the government–resident–contractor triad, how do multi-dimensional policy levers jointly determine the system’s evolutionary trajectories and stable equilibria?
• For resource allocation (w,v), cost sharing (p,q), and behavioral intervention (e,d), what critical thresholds and nonlinear effects emerge, and how do their interactions reshape the basins of attraction and the probabilities of convergence across equilibria?
• Confronting the common practical bottleneck (E₃)—characterized by proactive governments and contractors but indifferent residents—what phased policy portfolios can effectively steer the system toward the ideal three-party cooperative equilibrium?

This study not only provides an integrative theoretical lens for dissecting the complex dynamics of resident-led urban regeneration, but also, through evolutionary-game-based quantitative simulations, offers a systematic decision-support basis and a practical pathway for overcoming collective action dilemmas and formulating targeted urban regeneration policies.

2. Literature Review

2.1. Fragmentation of Policy Instruments for Resident-Led Urban Regeneration and the Absence of an Integrative Framework

In the global field of urban regeneration, resident-led urban regeneration—with communities as the principal actor—has been widely recognized as a critical pathway to sustainable development. Institutional practices exemplified by the United Kingdom’s Community Right to Build/Neighborhood Planning demonstrate that, once communities are endowed with statutory planning powers and resource-mobilization platforms, they can more effectively translate place-based demands into implementable project proposals and enhance the coordination and accessibility of the provision of housing and public facilities [35,36,37]. This top-down empowerment through legal statutes provides a stable institutional environment for community initiatives. In contrast, China’s practice of resident-led regeneration is primarily propelled by policy directives (e.g., the Guiding Opinions [15]) and characterized by localized, pilot-based experimentation, such as the Zhegong Xincun project [20,21]. This fundamental institutional difference—statutory entitlement versus policy-driven pilots—creates a distinct context where the coordination of interests among governments, residents, and contractors becomes even more critical and precarious due to the lack of a formalized legal framework for community power. Therefore, understanding and designing sophisticated policy levers to navigate this complex, dynamic interplay of interests is particularly necessary in the Chinese context. In the European context, policy frameworks for land regeneration and value capture are likewise deployed to support benefit alignment and risk sharing among communities, governments, and markets, thereby furnishing durable financial and governance support for resident-led urban regeneration at the grassroots [38,39,40].

In China, propelled by the Guiding Opinions on Comprehensively Advancing the Renovation of Old Urban Residential Communities and related provincial policies in Zhejiang, “resident-led urban regeneration” and “in-situ demolition-and-reconstruction” have ascended from local experimentation to the national strategic level. Case studies centered on Beijing’s Jinsong Model, Guangzhou’s Yongqing Fang renewal, and especially the area-wide renewal of Hangzhou’s Zhegong Xincun provide a rich body of empirical evidence [14,20,21].

Building on this, the academic literature has identified multiple policy instruments and assembled a preliminary policy “toolbox”. Among them, resource-allocation levers—such as floor area ratio (FAR) bonuses and transfer of development rights (TDRs)—incentivize the entry of private capital and community participation by creating incremental development value [35,38]. Cost-sharing levers, such as tax abatements, development-fee apportionment, and earmarked subsidies—are employed to ease actors’ cash-flow constraints and upfront contribution burdens, thereby enhancing project bankability and financial viability [38,40]. In parallel, “soft” interventions, such as community capacity building, scenario workshops, and public participation programs—help strengthen shared visioning, consensus around project proposals, and collaborative execution capacity, while bolstering communities’ organizational mobilization and learning capabilities [5,35,41].

However, a critical reading of this international literature reveals a salient theoretical limitation: existing studies tend to privilege disaggregation over integration. A substantial portion of the work either concentrates on the micro-level effects of a single instrument or remains at qualitative, macro-level principles, with limited effort to situate resource allocation, cost sharing, and behavioral intervention within a unified analytical framework—namely, an integrated policy-portfolio perspective—capable of systematically characterizing their interdependencies, synergistic effects, and potential antagonisms [35,40,42]. This fragmentation constrains the explanatory power for complex renewal practices and hampers the provision of clear design and implementation guidance for “precision policy portfolios” oriented toward specific objectives (e.g., overcoming bottlenecks to resident participation, improving coordination efficiency). It thereby underscores the necessity of coupling collaborative governance with integrated methodologies for policy-instrument design [38,43,44,45].

2.2. The Pivotal Role of Behavioral Economics in Decision-Making for Resident-Led Urban Regeneration

Behavioral economics—particularly Prospect Theory as established by Kahneman and Tversky—provides a robust foundation for understanding actual decision-making under uncertainty, thereby remedying the limited explanatory power of overly stringent full-rationality assumptions in urban regeneration governance [46,47]. In the context of resident-led urban regeneration, this theoretical framework explains residents’ widespread aversion to, and procrastination over, “certain expenditures-uncertain returns,” and furnishes operational micro-foundations for incorporating behavioral variables into evolutionary game models and policy-instrument design [47,48].

Reference dependence and loss aversion. Prospect Theory posits that individuals evaluate outcomes relative to a reference point—typically the status quo—and exhibit greater sensitivity to losses than to gains. Empirical measurements, particularly in contexts involving significant financial outlays, have estimated the loss aversion coefficient λ to commonly fall within a range of approximately 1.5 to 2.5 [49,50]. In the context of resident-led urban regeneration of old urban residential communities, requiring households to make substantial self-financing contributions (a certain “loss”) in exchange for prospective improvements in housing quality and safety (a probabilistic “gain”) is disproportionately amplified by loss aversion, thereby suppressing willingness to contribute and to collaborate [46,47,51]. To capture this behavioral regularity, we introduce the cost-burden perception coefficient e (e > 1), which scales the actual monetary cost in the resident’s payoff function, effectively modeling the amplified psychological weight of the upfront payment. The value of e is conceptually aligned with the empirically observed λ range. This implies that simply increasing the FAR uplift (area expansion coefficient) or the financial returns may not effectively overcome the participation barrier arising from the “pain of paying”; complementary behavioral interventions are needed to reshape the reference point and reframe mental accounts.

Nonlinear probability weighting. Cumulative Prospect Theory posits that individuals systematically overweight small probabilities and underweight moderate-to-high probabilities, thereby distorting subjective assessments of risk-return trade-offs [47,48,52]. In renewal practice, this helps explain why residents—even when confronted with objectively moderate-to-high-probability hazards, such as structural deterioration, fire, and earthquakes—may, owing to normalization and habituated low sensitivity, choose to ignore or postpone renovation decisions [53,54,55]. Consequently, merely issuing objective risk notifications and improving engineering/technical parameters is unlikely to materially elevate subjective risk perception and propensity to act; “soft” interventions—such as visualized risk communication, scenario-based drills, and social norm prompts—are needed to correct probability-weighting bias.

Inertia driven by preferences and cognitive biases. Behavioral regularities that accompany loss aversion and probability weighting—such as status quo bias and the endowment effect—further entrench inertia and procrastination in consensus formation and collective action, thereby reducing coordination efficiency and predictability within game dynamics [47]. A systematic characterization of these biases enables us to explicitly embed residents’ perceived contribution-burden coefficient e (capturing loss aversion and mental accounting) and accident-risk perception coefficient d (capturing probability weighting and risk perception) into the evolutionary game model, and, on this basis, to design behavioral instruments, such as nudges, default options, and staged commitments, thereby forming a policy portfolio that is complementary to resource-allocation and cost-sharing levers. For the purposes of this study, which aims to establish an integrated yet tractable policy framework, the core behavioral principles of loss aversion and probability weighting are operationalized through the scalar coefficients e and d. This provides a crucial balance between behavioral realism and model parsimony, allowing for clear interpretation of the policy levers.

Prospect Theory and its subsequent extensions not only offer a testable explanation for the “policy-hot, resident-cold” phenomenon, but also provide a mechanistic basis for modifying the “subjective utility function” through a portfolio of instruments: optimizing objective parameters (e.g., increasing w or reducing p) should proceed in parallel with behavioral interventions that reset the reference point, reduce the salience of losses, and calibrate probability weighting, thereby enhancing residents’ willingness to participate and to contribute financially, and ultimately improving the collaborative outcomes of resident-led urban regeneration.

2.3. Applications of the Evolutionary-Game Approach and Limitations in Integrating Behavioral Factors

Evolutionary Game Theory, via mechanisms such as replicator dynamics, models the strategy evolution of boundedly rational agents under repeated interaction and the stability of resulting equilibria. It has developed into a systematic methodology across public goods provision, environmental governance, and multi-actor coordination, demonstrating that institutional structure, information regimes, and sanctioning schemes materially shape cooperative steady states [56,57,58]. Within urban regeneration research, tripartite games (government-residents-contractors) are widely employed to analyze how incentives and regulation influence participation and collaboration: for example, some studies focus on the effects of government subsidies, FAR incentives (FAR uplift), and regulatory stringency on contractors’ and residents’ strategies, or characterize incentive-constraint interactions among government, energy service companies, and residents in green retrofits of existing buildings [26,59,60]. In parallel, resident-centered studies examine how alternative financing and contribution arrangements affect willingness to participate and the likelihood of project advancement, or use modeling and simulation to investigate the emergence and diffusion of cooperative behavior under neighborhood networks and social interactions. Nevertheless, notwithstanding these contributions, the existing evolutionary-game literature exhibits two salient shortcomings.

First, the paucity of research on policy-instrument portfolios. A substantial body of work tends to assess, in a single-instrument manner, the marginal effects of individual tools (e.g., fiscal subsidies or FAR incentives) within the policy toolbox, while overlooking the intrinsically portfolio-based nature of real-world interventions and the potential for nonlinear interactions and threshold effects among instruments. This constrains both the external validity and the operational applicability of findings to complex renewal practice [26,59,60]. Although recent studies have juxtaposed multi-actor games with financing mechanisms, regulatory strategies, or organizational collaboration, research that systematically couples and co-optimizes the three classes of instruments, “resource allocation-cost sharing-behavioral interventions”, remains limited, providing an insufficiently clear and structured foundation for designing a precision policy portfolio [26,61]. It is worth noting that the value of combining dynamic incentives with tripartite evolutionary game models has been demonstrated in adjacent fields, such as the electricity market, where such frameworks have been used to effectively study the co-evolution of market entities [62]. Our study contributes to this emerging stream of research by introducing and verifying a structured, multi-dimensional policy-lever system tailored to the complexities of urban regeneration.

Second, the over-rationalized treatment of behavior and perception. Although evolutionary games formally relax the assumption of full rationality, many models still specify payoff functions in which benefits and costs are treated as objective and readily monetizable quantities, adhering to a simple “gain-seeking/loss-avoiding” logic while seldom explicitly incorporating behavioral elements such as risk perception, loss aversion, and status quo bias. This underestimates the systematic influence on decision-making of housing’s dual character as both a high-value asset and a locus of emotional attachment [56,57]. A limited set of studies has attempted to embed Prospect Theory or subjective weights into tripartite evolutionary game models to account for residents’ financing and participation behaviors, showing that behavioral biases can substantially reshape equilibrium regions and convergence trajectories. Overall, however, the systematic quantification of behavioral factors and their explicit incorporation into game-theoretic payoff functions remains a frontier endeavor rather than common practice [23,24,63].

Furthermore, our study connects with two vibrant streams of the literature that employ evolutionary game theory. The first stream investigates fundamental mechanisms for promoting cooperation, such as peer punishment [64], prior commitments [65,66], and voluntary agreements [67,68]. The second demonstrates the tripartite model’s versatility in addressing modern governance challenges across diverse domains, including AI governance [69], environmental monitoring [70], healthcare investment [71], technology regulation [72], and energy policy [73]. While these studies validate the framework’s power, our contribution is to tailor it to the specific institutional and behavioral realities of resident-led urban regeneration. We introduce a novel multi-dimensional policy lever system that moves beyond examining single mechanisms or static incentives, instead offering a dynamic and integrated toolkit for steering the co-evolution of government, market, and resident strategies.

2.4. Innovations of This Study

In sum, while existing research has laid important groundwork, it still lacks a systematic analytical framework that integrates the three classes of policy instruments—resource allocation, cost sharing, and behavioral interventions—and explicitly characterizes their interaction effects: a “Multi-dimensional Policy Lever System”. The “Multi-dimensional Policy Lever System” developed herein is designed to fill this gap. The integrative framework—comprising resource-allocation levers (w,v), cost-sharing levers(p,q), and behavioral-intervention levers (e,d)—is not a simple superposition of prior studies, but a theoretical integration and innovation.

It aims to furnish a unifying theoretical lens for unpacking the complex dynamics of resident-led urban regeneration. By quantifying principles from behavioral economics and embedding them into game-theoretic payoff functions, it provides a more realistic micro-psychological foundation for understanding resident behavior; and through systematic numerical simulations, it reveals both the independent and joint effects of the various levers, thereby offering more systematic and targeted solutions and policy insights to resolve collective-action dilemmas and advance sustainable urban regeneration.

3. Building and Analysis of Evolutionary Game Model

3.1. Assumptions and Key Variables

As a framework for analyzing conflict and cooperation, game theory examines the strategic decision-making interactions among multiple stakeholders. Focusing on the context of resident-led urban regeneration in aging residential communities, this study develops a tripartite evolutionary game model involving government, residents, and contractors.

Assumption 1.

Each actor has two strategies. The government either implements a proactive guidance policy that supports residents in undertaking demolition-and-reconstruction of aging residential communities (x) or adopts a passive, laissez-faire stance (1 − x); residents either choose demolition-and-reconstruction (y) or opt for repair-and-beautification only (1 − y); contractors either actively support demolition-and-reconstruction (z) or treat demolition-and-reconstruction passively (1 − z). The strategy shares satisfy 0 ≤ x,y,z ≤ 1. All three parties are assumed to be risk-neutral with respect to the objective, nominal monetary flows. However, residents’ decisions are further shaped by bounded rationality, captured through the subjective cost-burden perception coefficient (e) and accident-risk perception coefficient (d), which distort the subjective utility derived from these monetary outcomes. There are eight possible strategy profiles across the three parties, as summarized in Table 1.

Table 1. The eight strategy profiles of the tripartite game.

Resident		In-Situ Demolition-and-Reconstruction (y)		Repair-and-Beautification (1 − y)
Contractor		Proactive Engagement (z)	Passive Response (1 − z)	Proactive Engagement (z)	Passive Response (1 − z)
Government	Proactive Guidance (x)	E1:(1,1,1)	E2:(1,1,0)	E3:(1,0,1)	E4:(1,0,0)
	Laissez-Faire (1 − x)	E5:(0,1,1)	E6:(0,1,0)	E7:(0,0,1)	E8:(0,0,0)

Assumption 2.

Depending on the scenario, the government obtains integrated benefits of urban regeneration B_g1~B_g4, incurs costs C_g1~C_g5, may suffer accident-handling and reputational losses C_g6 and C_g7, and grants subsidies R_g1-R_g3 to residents and contractors.

When the government implements the demolition-and-reconstruction policy (x), it grants residents an expansion quota equal to w times the original-area—including increases in in-unit area, common spaces, and garages—and incurs a capacity-expansion management cost C_g2. Under the strategy profile (1,1,1) (i.e., x = y = z = 1), the government allocates to contractors a share v of the urban development proceeds attributable to the expanded portion. By contrast, under (1,1,0), when contractors behave passively, the government does not transfer the expansion-related development proceeds to contractors; instead, it receives the expansion-related development revenue B_g3 and increases the subsidy to residents to R_g2. This formulation of B_g3 represents the government’s net economic benefit from the expansion area before any redistribution via the sharing coefficient v. The corresponding construction revenues and costs are accounted for solely in the contractor’s payoff, ensuring there is no double-counting between the actors’ accounts.

When the government adopts the repair-and-beautification policy (1 − x), it is willing to provide funding support for repair-and-beautification in aging residential communities; however, if residents choose demolition-and-reconstruction, the government permits rebuilding only up to the original-area (i.e., no expansion).

Assumption 3.

Depending on the scenario, residents obtain property appreciation benefits B_r1~B_r3; make out-of-pocket contributions to contractors C_r1~C_r4, with the residents’ perceived cost equal to the monetary outlay scaled by the cost-burden perception coefficient e; incur behavior-contingent base implementation costs C_r5 and C_r6; when opting for demolition-and-reconstruction, additionally bear temporary off-site living costs C_r7 during the rebuilding period; and, if accidents occur after repair-and-beautification of the aging residential community, suffer a loss C_r8.

When residents choose demolition-and-reconstruction (y), they pay contractors the corresponding demolition-and-reconstruction construction costs.

When residents choose repair-and-beautification (1 − y) while the government actively promotes the demolition-and-reconstruction policy, residents pay contractors the repair-and-beautification construction costs.

Assumption 4.

Depending on the scenario, contractors receive construction revenues B_v1–B_v3 and B_v7; obtain additional reputational benefits B_v5 or B_v6; pay construction costs C_v1, C_v2, or C_v4; incur base implementation costs C_v6 or C_v7; and, if accidents occur after repair-and-beautification, suffer reputational losses C_v8 or C_v9.

When contractors actively support demolition-and-reconstruction (z), and both the government and residents also take proactive actions, contractors receive a subsidy equal to a fraction v of the urban-development proceeds attributable to the expanded portion. Residents must pay the government an amount priced at p times the prevailing market housing price. For the original floor-area portion, the government requires contractors to charge residents reconstruction fees at q times the quoted reconstruction cost.

When contractors treat demolition-and-reconstruction passively (1 − z), construction fees are charged to residents or the government according to normal market construction quotations.

Assumption 5.

The payoff functions for all players integrate monetary terms (e.g., costs, revenues) with non-monetary benefits (e.g., social reputation). This formulation operates under the standard assumption in evolutionary game theory that decision-makers can subjectively weigh and aggregate these diverse outcomes into a common utility scale, which determines their strategic preferences [49]. The model’s focus on comparative strategy dynamics ensures that the insights regarding policy lever effects are robust to this assumption.

All parameter definitions are provided in Table 2. The basic assumptions are as follows:

Table 2. Assumed parameters in the evolutionary game model. (* indicates a value that could be either 1 or 0).

Parameter	Meaning	Remarks
H	Pre-renewal unit housing price in the aging community (10,000 CNY/m2).	H > 0
N	Average Original Building Area per Household of Old Residential Communities (m2).	N > 0
w	Area-expansion coefficient: ratio of added floor area to original area granted by the government under strategy profile (1,1,*), including in-unit area, garages, and other public spaces.	w ≥ 0
v	Expansion benefit-sharing coefficient: proportion of economic benefits from the expanded area shared by the government with the contractor under strategy profile (1,1,1).	0 ≤ v≤1
p	Expansion-purchase coefficient: proportion of the market price residents are required to pay for the expanded area under strategy profile (1,1,*).	p ≥ 0
q	Original-area reconstruction payment coefficient: discount ratio on the contractor’s quoted price for reconstructing the original area under strategy profile (*,1,1).	0 ≤ q≤1
e	Cost-burden perception coefficient of residents (e.g., when e = 1.8, the perceived financial pressure is 1.8 times the actual cost).	e > 0
d	Accident-risk perception coefficient of residents regarding the aging community.	d > 0
s	Objective probability of accidents occurring in the old housing under strategy profile (*,0,*).	0 ≤ s ≤ 1
k	Property value appreciation coefficient for the new, expanded housing under strategy profile (1,1,*).	k = u·wl
u	Intensity factor influencing the property value appreciation for the new, expanded housing.
l	Rate factor influencing the property value appreciation for the new, expanded housing.
j	Property value appreciation coefficient for the new housing without area expansion under strategy profile (0,1,*).	j ≥ 0
i	Property value appreciation coefficient for the old housing after repair-and-beautification under strategy profile (*,0,*).	i ≥ 0
m	Ratio of the contractor’s unit construction quotation for demolition-and-reconstruction to the original housing price under strategy profile (*,1,*).	m ≥ 0
r	Ratio of the contractor’s unit quotation for repair-and-beautification to the original housing price under strategy profile (*,0,*).	r ≥ 0
f	Ratio of the contractor’s unit construction cost for demolition-and-reconstruction to the original housing price under strategy profile (*,1,*).	f ≥ 0
g	Ratio of the contractor’s unit cost for repair-and-beautification to the original housing price under strategy profile (*,0,*).	g ≥ 0
o	Cost impact coefficient for the government’s infrastructure upgrade.
Bg1	Government’s integrated benefits (e.g., social reputation) under demolition-and-reconstruction strategy profile (1,1,*).	Bg1 > 0
Bg2	Government’s negative social reputation under demolition-and-reconstruction strategy profile (0,1,*).	Bg2 < 0
Bg3	Government’s economic benefits (e.g., taxes) from expansion development under strategy profile (1,1,*).	Bg3 = N·w·p·H·(1 + k) − Bv4·w·N
Bg4	Government’s integrated benefits (e.g., social reputation) under repair-and-beautification strategy profile (0,0,*).	Bg4 > 0
Cg1	Base implementation cost of the government’s Proactive Guidance policy under strategy profile (1,*,*).
Cg2	Infrastructure upgrade cost incurred by the government for granting the area expansion under strategy profile (1,1,*).	Cg2 = N·wo·Cg3
Cg3	Unit base cost for the government’s infrastructure upgrade.
Cg4	Policy execution cost under the government’s Laissez-faire strategy under strategy profile (0,*,*).
Cg5	Government’s payment to the contractor for repair-and-beautification under strategy profile (0,0,*).	Cg5 = Bv7
Cg6	Government’s accident handling cost and reputational loss when accidents occur after repair-and-beautification under strategy profile (0,0,*).
Cg7	Government’s accident handling cost and reputational loss when accidents occur after repair-and-beautification under strategy profile (1,0,*).
Rg1	Base subsidy from the government to residents under strategy profile (1,1,*).
Rg2	Additional subsidy from the government to residents under strategy profile (1,1,0).
Rg3	Subsidy (share of expansion development benefits) from the government to the contractor under strategy profile (1,1,1).	Rg3 = v·Bg3
Br1	Residents’ property appreciation benefits under demolition-and-reconstruction strategy profile (1,1,*).	Br1 = N·(1 + w)·H·(1 + k)-N·H
Br2	Residents’ property appreciation benefits under demolition-and-reconstruction strategy profile (0,1,*).	Br2 = N·H·j
Br3	Residents’ property appreciation benefits under repair-and-beautification strategy profile (*,0,*).	Br3 = N·H·i
Cr1	Residents’ contribution payment under demolition-and-reconstruction strategy profile (1,1,1).	Cr1 = p·N·w·H·(1 + k) + q·Bv4·N
Cr2	Residents’ contribution payment under demolition-and-reconstruction strategy profile (1,1,0).	Cr2 = p·N·w·H·(1 + k) + Bv4·N
Cr3	Residents’ contribution payment under demolition-and-reconstruction strategy profile (0,1,*).	Cr3 = Bv3
Cr4	Residents’ contribution payment under repair-and-beautification strategy profile (1,0,*).	Cr4 = Bv7
Cr5	Base implementation cost for residents’ demolition-and-reconstruction behavior under strategy profile (*,1,*).
Cr6	Base implementation cost for residents’ repair-and-beautification behavior under strategy profile (*,0,*).
Cr7	Temporary off-site living cost for residents during the demolition-and-reconstruction period under strategy profile (*,1,*).
Cr8	Loss to residents from accidents occurring after repair-and-beautification under strategy profile (*,0,*).
Bv1	Contractor’s construction quotation for the new project under Proactive Engagement and strategy profile (1,1,1).	Bv1 = Bv4·w·N + q·Bv4·N
Bv2	Contractor’s construction quotation for the new project under Passive Response and strategy profile (1,1,0).	Bv2 = N·(1 + w)·Bv4
Bv3	Contractor’s construction quotation for the new project under strategy profile (0,1,*).	Bv3 = N·Bv4
Bv4	Contractor’s unit area quotation for demolition-and-reconstruction (10,000 CNY/㎡) under strategy profile (*,1,*).	Bv4 = H·m
Bv5	Contractor’s additional reputational benefit under strategy profile (1,1,1).	Bv5 > Bv6
Bv6	Contractor’s additional reputational benefit under strategy profile (0,1,1).
Bv7	Contractor’s quotation for repair-and-beautification under strategy profile (*,0,*).	Bv7 = N·Bv8
Bv8	Contractor’s unit area quotation for repair-and-beautification (10,000 CNY/㎡) under strategy profile (*,0,*).	Bv8 = H·r
Cv1	Contractor’s construction cost for demolition-and-reconstruction under strategy profile (1,1,*).	Cv1 = N·(1 + w)·Cv3
Cv2	Contractor’s construction cost for demolition-and-reconstruction under strategy profile (0,1,*).	Cv2 = N·Cv3
Cv3	Contractor’s unit area construction cost for demolition-and-reconstruction (10,000 CNY/m2) under strategy profile (*,1,*).	Cv3 = H·f
Cv4	Contractor’s construction cost for repair-and-beautification under strategy profile (*,0,*).	Cv4 = N·Cv5
Cv5	Contractor’s unit area cost for repair-and-beautification (10,000 CNY/㎡) under strategy profile (*,0,*).	Cv5 = H·g
Cv6	Base implementation cost for the contractor’s Proactive Engagement under strategy profile (*,*,1).
Cv7	Base implementation cost for the contractor’s Passive Response under strategy profile (*,*,0).
Cv8	Reputational loss to the contractor when accidents occur after repair-and-beautification and under Proactive Engagement strategy profile (*,0,1).
Cv9	Reputational loss to the contractor when accidents occur after repair-and-beautification and under Passive Response strategy profile (*,0,0).

3.2. Establishing and Solving the Evolutionary Game Model

Based on the above assumptions and related variables, the pay-off matrix for the tripartite evolutionary game model is obtained Table 3.

Table 3. Pay-off matrix for the tripartite evolutionary game.

Resident		In-Situ Demolition-and-Reconstruction (y)		Repair-and-Beautification (1 − y)
Contractor		Proactive Engagement (z)	Passive Response (1 − z)	Proactive Engagement (z)	Passive Response (1 − z)
Government	Proactive Guidance (x)	Bg1 + Bg3-Cg1-Cg2-Rg1-Rg3	Bg1 + Bg3-Cg1-Cg2-Rg1-Rg2	-Cg1-s·Cg7	-Cg1-s·Cg7
		Br1-e·Cr1-Cr5-Cr7 + Rg1	Br1-e·Cr2-Cr5-Cr7 + Rg1 + Rg2	Br3-e·Cr4-Cr6-d·s·Cr8	Br3-e·Cr4-Cr6-d·s·Cr8
		Bv1 + Bv5-Cv1-Cv6 + Rg3	Bv2-Cv1-Cv7	Bv7-Cv4-Cv6-s·Cv8	Bv7-Cv4-Cv7-s·Cv9
	Laissez- Faire (1 − x)	Bg2-Cg4	Bg2-Cg4	Bg4-Cg4-Cg5-s·Cg6	Bg4-Cg4-Cg5-s·Cg6
		Br2-e·q·Cr3-Cr5-Cr7	Br2-e·Cr3-Cr5-Cr7	Br3-Cr5-d·s·Cr8	Br3-Cr5-d·s·Cr8
		(1-q)·Bv3 + Bv6-Cv2-Cv6	Bv3-Cv2-Cv7	Bv7-Cv4-Cv6-s·Cv8	Bv7-Cv4-Cv7-s·Cv9

Expected earnings from government’s active-guidance policies, E_g1:

E_g1 = y·z·(B_g1 + B_g3 − C_g1 − C_g2-R_g1-R_g3) + y·(1 − z)·(B_g1 + B_g3 − C_g1 − C_g2 − R_g1 − R_g2)
+ (1 − y)·z·(-C_g1-s·C_g7) + (1 − y)·(1 − z)·(-C_g1-s·C_g7)

(1)

Expected earnings from government’s passive approaches, E_g2:

E_g2 = y·z·(B_g2 − C_g4) + y·(1 − z)·(B_g2 − C_g4) + (1 − y)·z·(B_g4 − C_g4 − C_g5 − s·C_g6) + (1 − y)·(1 − z)·(B_g4 − C_g4 − C_g5 − s·C_g6)

(2)

Mean expected earnings for government, E_g3:

E_g3 = x·E_g1 + (1 − x)·E_g2

(3)

Replicator dynamic equation for local government’s policies, F(x) = x·(E_g1 − E_g3), where

F(x) = x·(1 − x)·((y·z·(B_g1 + N·w·H·(p·(1 + u·w^l)-m)-C_g1-N·w^o·C_g3-R_g1-v·N·w·H·(p·(1 + u·w^l)-m))
+ y·(1 − z)·(B_g1 + N·w·H·(p·(1 + u·w^l)-m)-C_g1-N·w^o·C_g3-R_g1-R_g2)
+ (1 − y)·z·(-C_g1-s·C_g7) + (1 − y)·(1 − z)·(-C_g1-s·C_g7))-(y·z·(B_g2-C_g4) + y·(1 − z)·(B_g2-C_g4)
+ (1 − y)·z·(B_g4-C_g4-N·H·r-s·C_g6) + (1 − y)·(1 − z)·(B_g4-C_g4-N·H·r-s·C_g6)))

(4)

Expected earnings from residents’ high-quality operations-oriented regeneration, E_r1:

E_r1 = x·z·(B_r1-e·C_r1-C_r5-C_r7 + R_g1) + (1 − x)·z·(B_r2-e·C_r3-C_r5-C_r7)
+ x·(1 − z)·(B_r1-e·C_r2-C_r5-C_r7 + R_g1 + R_g2) + (1 − x)·(1 − z)·(B_r2-e·C_r3-C_r5-C_r7)

(5)

Expected earnings from residents’ low-quality repair-and-beautification, E_r2:

E_r2 = x·z·(B_r3-e·C_r4-C_r6-d·s·C_r8) + (1 − x)·z·(B_r3-C_r5-d·s·C_r8)
+ x·(1 − z)·(B_r3-e·C_r4-C_r6-d·s·C_r8) + (1 − x)·(1 − z)·(B_r3-C_r5-d·s·C_r8)

(6)

Mean expected earnings for residents, E_r3:

E_r3 = y·E_r1 + (1 − y)·E_r2

(7)

Replicator dynamic equation for residents’ investments F(y) = y·(E_r1 − E_r3), where

F(y) = y·(1 − y)·((x·z·(N·H·(w + u·w^l + w·u·w^l)-e·(p·N·w·H·(1 + u·w^l) + q·H·m·N)
-C_r5-C_r7 + R_g1) + (1 − x)·z·(N·H·j-e·q·N·H·m-C_r5-C_r7) + x·(1 − z)·(N·H·(w + u·w^l + w·u·w^l)
-e·(p·N·w·H·(1 + u·w^l) + H·m·N)-C_r5-C_r7 + R_g1 + R_g2) + (1 − x)·(1 − z)·(N·H·j-e·N·H·m-C_r5-C_r7))
-(x·z·(N·H·i-e·N·H·r-C_r6-d·s·C_r8) + (1 − x)·z·(N·H·i-C_r5-d·s·C_r8)
+ x·(1 − z)·(N·H·i-e·N·H·r-C_r6-d·s·C_r8) + (1 − x)·(1 − z)·(N·H·i-C_r5-d·s·C_r8)))

(8)

Expected earnings from contractors’ active responses, E_v1:

E_v1 = x·y·(B_v1 + B_v5-C_v1-C_v6 + R_g3) + (1 − x)·y·((1-q)*B_v3 + B_v6-C_v2-C_v6)
+ x·(1 − y)·(B_v7-C_v4-C_v6-s·C_v8) + (1 − x)·(1 − y)·(B_v7-C_v4-C_v6-s·C_v8)

(9)

Expected earnings from contractors’ passive responses, E_v2:

E_v2 = x·y·(B_v2-C_v1-C_v7) + (1 − x)·y·(B_v3-C_v2-C_v7) + x·(1 − y)·(B_v7-C_v4-C_v7-s·C_v9)
+ (1 − x)·(1 − y)·(B_v7-C_v4-C_v7-s·C_v9)

(10)

Mean expected earnings for contractors, E_v3:

E_v3 = z·E_v1 + (1 − z)·E_v2

(11)

Replicator dynamic equation for contractors’ responses F(z) = z·(E_v1 − E_v3), where

F(z) = z·(1 − z)·((x·y·((H·m·w·N + q·H·m·N) + B_v5-N·(1 + w)·H·f-C_v6 + v·N·w·H·(p·(1 + u·w^l)-m))
+ (1 − x)·y·((1-q)·N·H·m + B_v6-N·H·f-C_v6) + x·(1 − y)·(N·H·r-N·H·g-C_v6-s·C_v8)
+ (1 − x)·(1 − y)·(N·H·r-N·H·g-C_v6-s·C_v8))-(x·y·(N·(1 + w)·H·m-N·(1 + w)·H·f-C_v7)
+ (1 − x)·y·(N·H·m-N·H·f-C_v7) + x·(1 − y)·(N·H·r-N·H·g
-C_v7-s·C_v9) + (1 − x)·(1 − y)·(N·H·r-N·H·g-C_v7-s·C_v9)))

(12)

3.3. Analysis of Points of Equilibrium Under Evolutionarily Stable Strategy

Setting the replicator dynamic equations f(x), f(y), and f(z) of the tripartite evolutionary game model to zero yields eight potential equilibrium points: E₁(1,1,1), E₂(1,1,0), E₃(1,0,1), E₄(1,0,0), E₅(0,1,1), E₆(0,1,0), E₇(0,0,1), and E₈(0,0,0) [74,75,76].

The stability of each equilibrium point in this system of differential equations is determined by the eigenvalues of the corresponding Jacob matrix. For the tripartite game, the Jacob matrix is defined as follows:

$$\mathrm{J}=\left\{\begin{array}{c}\begin{array}{ccc}{\displaystyle \frac{\mathrm{\partial }F\left(x\right)}{\mathit{dx}}}& {\displaystyle \frac{\mathrm{\partial }F\left(x\right)}{\mathit{dy}}}& {\displaystyle \frac{\mathrm{\partial }F\left(x\right)}{\mathit{dz}}}\\ {\displaystyle \frac{\mathrm{\partial }F\left(y\right)}{\mathit{dx}}}& {\displaystyle \frac{\mathrm{\partial }F\left(y\right)}{\mathit{dy}}}& {\displaystyle \frac{\mathrm{\partial }F\left(y\right)}{\mathit{dz}}}\\ {\displaystyle \frac{\mathrm{\partial }F\left(z\right)}{\mathit{dx}}}& {\displaystyle \frac{\mathrm{\partial }F\left(z\right)}{\mathit{dy}}}& {\displaystyle \frac{\mathrm{\partial }F\left(z\right)}{\mathit{dz}}}\end{array}\end{array}\right.=\left\{\begin{array}{c}\begin{array}{ccc}(2\mathrm{x}-1)·\mathrm{g}\left(1\right)& \mathrm{x}·(\mathrm{x}-1)·\mathrm{g}(2)& \mathrm{x}·(1-\mathrm{x})·\mathrm{g}(3)\\ \mathrm{y}·(1-\mathrm{y})·\mathrm{g}(4)& (1-2\mathrm{y})·\mathrm{g}(5)& \mathrm{y}·(\mathrm{y}-1)·\mathrm{g}(6)\\ \mathrm{z}·(1-\mathrm{z})·\mathrm{g}(7)& \mathrm{z}·(1-\mathrm{z})·\mathrm{g}(8)& (1-2\mathrm{z})·\mathrm{g}(9)\end{array}\end{array}\right.$$

(13)

where:

g(1) = B_g4 + C_g1-C_g4-C_g6·s + C_g7·s-B_g1·y + B_g2·y-B_g4·y + R_g1·y + R_g2·y-H·N·r + C_g6·s·y-C_g7·s·y-R_g2·y·z + C_g3·N·w^o·y + H·N·r·y + H·N·m·w·y-H·N·p·w·y-H·N·k·p·w·y-H·N·m·v·w·y·z + H·N·p·v·w·y·z + H·N·k·p·v·w·y·z

g(2) = B_g2-B_g1-B_g4 + R_g1 + R_g2 + C_g6·s-C_g7·s-R_g2·z + H·N·r + C_g3·N·w^o + H·N·m·w-H·N·p·w-H·N·k·p·w-H·N·m·v·w·z + H·N·p·v·w·z + H·N·k·p·v·w·z

g(3) = y·(R_g2 + H·N·m·v·w-H·N·p·v·w-H·N·k·p·v·w)

g(4) = C_r6-C_r5 + R_g1 + R_g2-R_g2·z-H·N·j + H·N·k + H·N·w + H·N·e·r + H·N·k·w-H·N·e·p·w-H·N·e·k·p·w

g(5) = C_r6·x-C_r5·x-C_r7 + R_g1·x + R_g2·x-H·N·i + H·N·j + C_r8·d·s-R_g2·x·z-H·N·e·m-H·N·j·x + H·N·k·x + H·N·w·x + H·N·e·m·z + H·N·e·r·x + H·N·k·w·x-H·N·e·m·q·z-H·N·e·p·w·x-H·N·e·k·p·w·x

g(6) = R_g2·x-H·N·e·m + H·N·e·m·q

g(7) = y·(B_v5-B_v6-H·N·m + 2·H·N·m·q-H·N·m·v·w + H·N·p·v·w + H·N·k·p·v·w)

g(8) = B_v6 + C_v8·s-C_v9·s + B_v5·x-B_v6·x-H·N·m·q-H·N·m·x + 2·H·N·m·q·x-H·N·m·v·w·x + H·N·p·v·w·x + H·N·k·p·v·w·x

g(9) = C_v7-C_v6-C_v8·s + C_v9·s + B_v6·y + C_v8·s·y-C_v9·s·y + B_v5·x·y-B_v6·x·y-H·N·m·q·y-H·N·m·x·y + 2·H·N·m·q·x·y-H·N·m·v·w·x·y + H·N·p·v·w·x·y + H·N·k·p·v·w·x·y

The stability of each equilibrium point in this system of differential equations is determined by the eigenvalues of the corresponding Jacobian matrix. Following the standard methodology in evolutionary game theory, an equilibrium is classified as locally asymptotically stable if all three eigenvalues of the Jacobian matrix have negative real parts, whereas it is unstable if at least one eigenvalue has a positive real part [76]. The eigenvalues λ for all eight candidate equilibria are summarized in Table 4.

Table 4. Eigenvalues of the eight pure-strategy equilibrium points and their stability conditions (an equilibrium is locally asymptotically stable if all three eigenvalues have negative real parts).

ESS	λ1	λ2	λ3
E1 (1,1,1)	Bg2-Bg1 + Cg1-Cg4 + Rg1 + Cg3·N·wo + H·N·w·(m-p·(k + 1)) − H·N·v·w·(m-p·(k + 1))	Cr5-Cr6 + Cr7-Rg1 + e·(H·N·m·q + H·N·p·w·(k + 1)) + H·N·i-H·N·(k + w+k·w) − Cr8·d·s-H·N·e·r	Cv6-Bv5-Cv7 + H·N·m·(w + 1) − H·N·m·q-H·N·m·w + H·N·v·w·(m-p·(k + 1))
E2 (1,1,0)	Cg3·N·wo + H·N·(m-p·(k + 1))·w-Bg1 + Bg2 + Cg1-Cg4 + Rg1 + Rg2	Cr5-Cr6 + Cr7-Rg1-Rg2 + e·(H·N·m + H·N·p·w·(k + 1)) + H·N·i-H·N·(k + w+k·w)-Cr8·d·s-H·N·e·r	Bv5-Cv6 + Cv7-H·N·m·(w + 1) + H·N·m·q + H·N·m·w-H·N·v·w·(m-p·(k + 1))
E3 (1,0,1)	Bg4 + Cg1-Cg4-Cg6·s + Cg7·s-H·N·r	Cr6-Cr5-Cr7 + Rg1-e·(H·N·m·q + H·N·p·w·(k + 1))-H·N·i + H·N·(k + w+k·w) + Cr8·d·s + H·N·e·r	Cv6-Cv7 + Cv8·s-Cv9·s
E4 (1,0,0)	Bg4 + Cg1-Cg4-Cg6·s + Cg7·s-H·N·r	Cr6-Cr5-Cr7 + Rg1 + Rg2-e·(H·N·m + H·N·p·w·(k + 1))-H·N·i + H·N·(k + w+k·w) + Cr8·d·s + H·N·e·r	Cv7-Cv6-Cv8·s + Cv9·s
E5 (0,1,1)	Bg1-Bg2-Cg1 + Cg4-Rg1-Cg3·N·wo-H·N·w·(m-p·(k + 1)) + H·N·v·w·(m-p·(k + 1))	Cr7 + H·N·i-H·N·j-Cr8·d·s + H·N·e·m·q	Cv6-Bv6-Cv7 + H·N·m + H·N·m·(q-1)
E6 (0,1,0)	Bg1-Cg3·N·wo-H·N·(m-p·(k + 1))·w-Bg2-Cg1 + Cg4-Rg1-Rg2	Cr7 + H·N·i-H·N·j-Cr8·d·s + H·N·e·m·q	Bv6-Cv6 + Cv7-H·N·m-H·N·m·(q-1)
E7 (0,0,1)	Cg4-Cg1-Bg4 + Cg6·s-Cg7·s + H·N·r	H·N·j-H·N·i-Cr7 + Cr8·d·s-H·N·e·m·q	Cv6-Cv7 + Cv8·s-Cv9·s
E8 (0,0,0)	Cg4-Cg1-Bg4 + Cg6·s-Cg7·s + H·N·r	H·N·j-H·N·i-Cr7 + Cr8·d·s-H·N·e·m·q	Cv7-Cv6-Cv8·s + Cv9·s

Completeness of Equilibrium Analysis. While the eight pure-strategy combinations at the vertices of the strategy space are the most salient equilibrium candidates, we have comprehensively analyzed the entire system for mixed-strategy equilibria (where 0 < x, y, z < 1) and equilibria on the edges and faces of the strategy cube. The structure of the replicator dynamics (Equations (4), (8) and (12)) reveals that the mixed-strategy equilibria, where they exist, are non-robust and fail to meet the criterion of local asymptotic stability (i.e., they are not evolutionarily stable states in the dynamic sense). This is a common outcome in complex multi-player evolutionary games with linear expected payoffs. Consequently, the asymptotically stable states of our system—which represent the long-term outcomes of the evolutionary process—are necessarily found among the eight pure-strategy profiles E1 to E8. This theoretical finding validates our subsequent focus on these points and is unequivocally supported by the numerical simulations presented in Section 4, all of which converge to one of these vertices.

Clarification of Equilibrium Concepts. It is important to distinguish between the concepts used in our analysis. An Evolutionarily Stable Strategy (ESS) is a strategic profile that, if adopted by a population, cannot be invaded by any alternative strategy that is initially rare. However, the replicator dynamic provides a specific process of strategy evolution. In this context, we analyze the local asymptotic stability of the fixed points of this dynamic system [76]. A fixed point is locally asymptotically stable if the system returns to it after any small perturbation. While an ESS is always a stable fixed point of the replicator dynamic in two-player symmetric games, this equivalence does not generally hold for multi-population games like our tripartite model [76]. Therefore, the focus of our stability analysis is on identifying the locally asymptotically stable fixed points of the replicator dynamics, which represent the robust long-term outcomes of the evolutionary process in our specific context. These stable states are the ones of primary practical interest for policy design.

Building on the eigenvalue analysis of the eight equilibrium points, we identify six key parameters—the area-expansion coefficient (w), the expansion-purchase coefficient (p), the original-area reconstruction payment coefficient (q), the expansion benefit-sharing coefficient (v), the cost-burden perception coefficient (e), and the accident-risk perception coefficient (d)—as the core building blocks of a multi-dimensional policy-lever system that jointly and systematically govern the evolutionary dynamics of government–resident–contractor strategies. Accordingly, we infer that the advancement of resident-led urban regeneration of aging residential communities in China may proceed through three canonical evolutionary phases, as shown in Figure 1, each corresponding to a distinct stable equilibrium, reflecting variation in the degree of coordination within the policy-lever system and in overall system efficiency.

Figure 1. Path diagrams based on tripartite evolutionary game model in the (a) initiation phase, (b) growth phase, and (c) maturation phase.

• Initiation phase: Systemic Stalemate (stable at E₈(0,0,0))

At this stage, the multi-dimensional policy-lever system is either not yet established or is severely misaligned. Resource-allocation levers (e.g., the area-expansion coefficient w and the expansion benefit-sharing coefficient v) are conservatively calibrated, depressing residents’ perceived asset-appreciation returns while leaving contractors without effective profit incentives. Cost-sharing levers (e.g., the expansion-purchase coefficient p and the original-area reconstruction payment coefficient q) are absent or mismatched, exposing residents to prohibitively high out-of-pocket contributions. More importantly, behavioral-intervention levers are effectively disregarded: residents’ perceived cost burden remains unaddressed (a high e), while recognition of accident risks in aging residential communities is largely neglected (a low d).

As a result, the expected payoff from any proactive strategy is substantially lower than that of maintaining the status quo, locking the system into the low-level equilibrium E₈(0,0,0)—a tripartite collective-action stalemate in which all three parties remain passive—thereby preventing resident-led urban regeneration projects from initiating.

• Growth phase: Resident Participation Bottleneck (stable at E₃(1,0,1))

This stage marks the initial activation of policy intervention, yet the deployment of levers remains uneven. Resource-allocation levers (e.g., a moderate increase in the expansion benefit-sharing coefficient v) coupled with the government’s ancillary infrastructure commitments successfully incentivize contractors to act proactively (z = 1). In parallel, cost-sharing levers begin to emerge in the marketplace (e.g., a more favorable original-area reconstruction payment coefficient q offered by contractors).

However, the policy mix exhibits a salient shortcoming: behavioral-intervention levers targeting residents are missing or insufficiently potent. Although the objective policy environment improves, residents’ perceived contribution burden remains elevated—i.e., the cost-burden perception coefficient stays high (e high)—and is not effectively mitigated through financial instruments. Meanwhile, their perception of accident risks also remains muted—i.e., the accident-risk perception is still low (d low).

Consequently, residents continue to prefer the lower-cost repair-and-beautification strategy, and the system stabilizes at the equilibrium E₃(1,0,1). This configuration—“government and contractors proactive while residents remain indifferent” (x = 1, z = 1, y = 0)—is the most commonly observed predicament in resident-led urban regeneration of aging residential communities.

• Maturation phase: Realization of Collaborative Governance (stable at E₁(1,1,1))

This stage represents the coordinated optimization of the multi-dimensional policy-lever system. Resource-allocation levers (w,v) achieve a finely tuned balance between enhancing residents’ sense of gain and safeguarding the fiscal sustainability of both the government and contractors. Cost-sharing levers (p,q), operationalized through a combined scheme of government tax relief and contractor price concessions, substantially lower residents’ effective out-of-pocket threshold.

Crucially, behavioral-intervention levers are deployed effectively: long-term, low-interest financing instruments bring the cost-burden perception coefficient e down into a rational range, while transparent risk assessment and communication strategies elevate the accident-risk perception coefficient d to a decision-salient threshold.

As a result, proactive strategies by all three parties form a positive reinforcement loop, and the system stabilizes at the desired equilibrium E₁(1,1,1), marking the maturation of a sustainable governance regime characterized by government guidance, market operation, and resident participation.

4. Simulation Results and Analysis

Advancing the smooth implementation of resident-led urban regeneration in China’s aging residential communities is a core objective of the country’s urban regeneration agenda and can enhance the payoffs of all stakeholders. Accordingly, this study takes the Mature Stage’s stable equilibrium E₁(1,1,1) as the focal state and employs MATLAB R2024b to conduct numerical simulations of the evolutionary trajectories of each party in the tripartite (government–resident–contractor) game, thereby providing an intuitive visualization of how key factors within the replicator-dynamics system shape the evolutionary process and outcomes.

4.1. Principles for Parameter Value Assignment and Calibration Strategy

The tripartite evolutionary game model incorporates parameters that can be classified into three categories for the purpose of calibration: (i) Core case-based parameters: directly informed by empirical data from representative projects (e.g., H, N, w, p). (ii) Behavioral parameters: grounded in established theories and empirical estimates from behavioral economics (e.g., e, d). (iii) Contextual and relational parameters: calibrated via simulation to ensure the model replicates plausible and stable equilibria under the baseline scenario, based on ranges suggested by the literature (e.g., B_g1, C_r5). This multi-source approach ensures the model is both empirically grounded and capable of generating the rich dynamics necessary to address our research questions. The baseline values and sources for all parameters are summarized in Table 5, and the detailed principles for each category are elaborated below.

Table 5. Assumptions of initial parameter values before simulation.

Parameter	H	N	w	v	p	q	e	l	u	j	i	m	r
Value	3.43	77	0.3	0.4	0.8	0.5	1.7	0.3	0.72	0.3	0.08	0.2	0.015
Parameter	f	g	s	d	o	Bg1	Bg2	Bg4	Cg1	Cg3	Cg4	Cg6	Cg7
Value	0.16	0.01	0.1	0.3	3	20	−15	2	2	26	0.5	10	6
Parameter	Rg1	Rg2	Cr5	Cr6	Cr7	Cr8	Bv5	Bv6	Cv6	Cv7	Cv8	Cv9
Value	2	10	5	0.5	15	200	20	4	2	0.4	10	4

(1) Core economic and physical parameters: based on representative practice cases

The model’s baseline economic and physical parameters are primarily informed by representative practices of resident-led urban regeneration in aging residential communities in China, with a particular focus on Zhejiang Province. The pre-renewal unit housing price (H = 3.43 represents 34,300 CNY/m²), original-area (N = 77 m²), area-expansion coefficient (w = 0.3), expansion-purchase coefficient (p = 0.8), and the contractor’s unit construction quotation and cost coefficients (m = 0.2, f = 0.16) are primarily sourced from publicly available market data and unit-type information for Hangzhou’s Zhegong Xincun project [20,21]. Similarly, the government’s unit infrastructure upgrade cost C_g3 = 26 is calibrated based on the approximate unit cost standards for public infrastructure in Hangzhou municipalities.

(2) Behavioral perception parameters: informed by behavioral economics theory and evidence.

Cost-burden perception coefficient e = 1.7. Setting e > 1 quantifies the loss-aversion effect in prospect theory. Classic and subsequent measurement studies show that individuals are typically more sensitive to losses than to commensurate gains in terms of subjective utility; commonly estimated loss-aversion parameters λ fall in the range of approximately 1.5~2.5, with early experiments yielding a benchmark of λ ≈ 2.25. In resident-led urban regeneration—where substantial, certain cash outlays are exchanged for probabilistic future improvements—loss aversion amplifies the “pain of paying,” thereby dampening residents’ willingness to contribute and to cooperate [46,48,49]. In conjunction with publicly available market data from Hangzhou’s Zhegong Xincun project [20,21], setting e = 1.7 is consistent with empirical findings on mental accounting in major household financial decisions.

Accident-risk perception coefficient d = 0.3. Setting d < 1 captures the systematic underweighting of medium-to-high probability events under the cumulative prospect theory framework—i.e., the subjective attenuation of objectively medium-to-high probability risks. Extensive evidence indicates that the canonical probability-weighting function is inverse-S-shaped: it overweighs small probabilities and underweighs medium-to-high probabilities [48,50]. In the context of “slow-moving, normalized risks” such as safety hazards in aging housing, and in the absence of effective risk communication and contextual cues, residents often exhibit insufficient risk perception and delayed action [77]. Accordingly, d = 0.3 is adopted as a baseline reduction coefficient for the subjective weighting of medium-to-high probability risks, reasonably reflecting the persistently low weights and “normalization-by-neglect” documented in empirical studies.

(3) Policy and relational parameters: determined via simulation-based calibration

For parameters that cannot be directly inferred from a single public source—such as government subsidies (R_g1, R_g2), the parties’ baseline implementation costs (C_g1, C_v6, C_r5, etc.), and the influence coefficients in the house-price appreciation function k = u·w^l (with u = 0.72, l = 0.3)—we first delimit plausible ranges by consulting the extant literature on the economic feasibility of urban regeneration projects [20,21]. The contractor’s reputational benefit B_v5 = 20 is set considering the significant non-financial incentives discussed in Gao et al. [26]. Building on this, we conduct preliminary simulations of the model’s dynamics to iteratively tune these parameters.

The core principle and objective of this tuning are the following: while preserving economically meaningful interpretations for all parameters, ensure that the model, under the baseline parameter set, admits a stable and theoretically desirable equilibrium E₁(1,1,1), while alternative equilibria (e.g., E₃, E₈) also emerge under specific parameter conditions. This procedure enables the model to generate theoretically consistent, richly featured evolutionary dynamics and provides a robust, reliable baseline scenario for subsequent sensitivity analysis—rather than mere numerical curve-fitting.

4.2. Area-Expansion Coefficient (w)

We sequentially set w to 0.1, 0.2, 0.3, 0.4, and 0.5 and obtain behavioral evolutionary simulations of how different area-expansion coefficients affect the three parties’ strategies, as shown in Figure 2: panel (a) presents the government’s behavioral evolution, panel (b) the residents’, and panel (c) the contractor’s.

Figure 2. Evolutionary trajectories of strategies under different w. The initial strategy proportions are (x_0, y_0, z₀) = (0.5, 0.5, 0.5). (a) Government’s strategy x. (b) Residents’ strategy y. (c) Contractor’s strategy z. The specific values of w for each trajectory are 0.1, 0.2, 0.3, 0.4, and 0.5, as indicated in the legend. The X-axis, “Time (Simulation Steps)”, represents the iteration steps in the numerical simulation.

As a core resource-allocation lever, the area-expansion coefficient w exhibits pronounced nonlinear and threshold effects in the simulations (Figure 2). When w is too low (=0.1), residents’ capital-gain benefits fail to offset their perceived costs, so their strategy rapidly converges to non-participation (y = 0), driving the entire system into the stalemate E₈(0,0,0). When w increases to a reasonable band (0.2~0.3), the payoff functions of all three parties are improved, and the system converges at a relatively high rate to the desired equilibrium E₁(1,1,1). However, when w is excessively high (= 0.5), residents’ objective returns rise but their actual cash outlay and perceived burden e surge, suppressing participation; simultaneously, the government’s complementary (co-financing) costs C_g2 escalate sharply, shifting its strategy toward disengagement and precipitating a breakdown of cooperation.

This inverted-U relationship indicates that a larger w is not necessarily better. Policy design must strike a fine balance between residents’ perceived gains, the government’s fiscal capacity, and the neighborhood’s physical carrying capacity, thereby providing a critical quantitative basis for floor-area-ratio (FAR) incentive policy.

4.3. Expansion Benefit-Sharing Coefficient (v)

We sequentially set v to 0.0, 0.2, 0.4, 0.6, and 0.8 and obtain behavioral evolutionary simulations of how different benefit-sharing ratios for expansion gains affect the three parties’ strategies, as shown in Figure 3: panel (a) presents the government’s behavioral evolution, panel (b) the residents’, and panel (c) the contractor’s.

Figure 3. Evolutionary trajectories of strategies under different v. The initial strategy proportions are (x_0, y_0, z₀) = (0.5, 0.5, 0.5). (a) Government’s strategy x. (b) Residents’ strategy y. (c) Contractor’s strategy z. The specific values of v for each trajectory are 0.0, 0.2, 0.4, 0.6, and 0.8, as indicated in the legend. The X-axis, “Time (Simulation Steps)”, represents the iteration steps in the numerical simulation.

The simulation results for the expansion benefit-sharing coefficient v (Figure 3) reveal a dual-threshold effect in aligning government-contractor interests. When v < 0.4, the contractor’s profit share is insufficient, and its strategy consistently converges to passive response z = 0. When v enters the reasonable band of 0.4~0.6, the contractor receives adequate marginal incentives and rapidly switches to active participation z = 1; simultaneously, the government, benefiting from the project’s aggregate positive effects (B_g1 + B_g3), maintains an active strategy x = 1, allowing the system to converge to the desired equilibrium E₁(1,1,1). However, when v is excessively high (=0.8), the government’s net payoff is overly compressed, prompting a swift shift to disengagement x = 0, which in turn erodes the contractor’s core incentives and precipitates a systemic breakdown of cooperation.

This nonlinear relationship substantiates the incentive-compatibility principle in evolutionary games. The optimal v does not unilaterally maximize any single party’s payoff; rather, it should approximate a Nash bargaining solution that balances the long-term interests of all three parties. This provides critical guidance for designing sustainable government-contractor partnership financial models.

4.4. Expansion-Purchase Coefficient (p)

We sequentially set p to 0.6, 0.7, 0.8, 0.9, and 1.0 and obtain behavioral evolutionary simulations of how different market-price purchase ratios for the added floor area affect the three parties’ strategies, as shown in Figure 4: panel (a) presents the government’s behavioral evolution, panel (b) the residents’, and panel (c) the contractor’s.

Figure 4. Evolutionary trajectories of strategies under different p. The initial strategy proportions are (x_0, y_0, z₀) = (0.5, 0.5, 0.5). (a) Government’s strategy x. (b) Residents’ strategy y. (c) Contractor’s strategy z. The specific values of p for each trajectory are 0.6, 0.7, 0.8, 0.9, and 1.0, as indicated in the legend. The X-axis, “Time (Simulation Steps)”, represents the iteration steps in the numerical simulation.

The simulation results for the expansion-purchase coefficient p (Figure 4) highlight its role as a cost-sharing lever and the inherent trade-off between residents’ willingness to participate and the project’s economic viability. The residents’ strategy y exhibits high price elasticity, decreasing monotonically as p rises. When p ≤ 0.8, property value appreciation offsets residents’ perceived costs, and the system can converge to the desired equilibrium E₁(1,1,1). Once p > 0.8, the perceived burden e amplifies cost pressures, inducing exit from cooperation (y→0). By contrast, the government’s and the contractor’s payoffs are positively related to p; excessively low p undermines their financial sustainability. This countervailing relationship pinpoints the core policy problem: identify a critical value of p that simultaneously satisfies residents’ participation threshold and preserves the project’s economic dynamism (approximately 0.8 in this study). The finding underscores the necessity of precise price-subsidy instruments to unlock the renewal impasse.

4.5. Original-Area Reconstruction Payment Coefficient (q)

We sequentially set q to 0.1, 0.3, 0.5, 0.7, and 0.9 and obtain behavioral evolutionary simulations of how different discount ratios on the quoted price for reconstructing the original-area affect the three parties’ strategies, as shown in Figure 5: panel (a) presents the government’s behavioral evolution, panel (b) the residents’, and panel (c) the contractor’s.

Figure 5. Evolutionary trajectories of strategies under different q. The initial strategy proportions are (x_0, y_0, z₀) = (0.5, 0.5, 0.5). (a) Government’s strategy x. (b) Residents’ strategy y. (c) Contractor’s strategy z. The specific values of q for each trajectory are 0.1, 0.3, 0.5, 0.7, and 0.9, as indicated in the legend. The X-axis, “Time (Simulation Steps)”, represents the iteration steps in the numerical simulation.

As a direct pricing instrument offered by the contractor, the Original-Area Reconstruction Payment Coefficient q reveals—in the simulations (Figure 5)—the pivotal role of a pricing-for-volume market strategy in activating resident demand. The residents’ strategy y is highly sensitive to q: willingness to participate rises markedly as q increases (i.e., as the out-of-pocket share declines). When q < 0.5, residents reject participation due to excessive effective costs; when q ≥ 0.5, their strategy evolves toward active participation.

The contractor’s strategy exhibits a nonlinear response. Its payoff is jointly shaped by q (affecting the unit price) and y (affecting transaction volume), achieving an optimal balance around q = 0.5. At this point, a moderate concession suffices to unlock resident participation; scaling up volume compensates for thinner unit margins, thereby maximizing aggregate payoff. This finding clarifies the necessity for the contractor to offer moderate price concessions (q ≥ 0.5) to jump-start the market and realize multi-party win-wins.

4.6. Cost-Burden Perception Coefficient (e)

We sequentially set e to 1.0, 1.5, 1.6, 1.7, and 1.8 and obtain behavioral evolutionary simulations of how different residents’ cost-burden perception coefficients affect the three parties’ strategies, as shown in Figure 6: panel (a) presents the government’s behavioral evolution, panel (b) the residents’, and panel (c) the contractor’s.

Figure 6. Evolutionary trajectories of strategies under different e. The initial strategy proportions are (x_0, y_0, z₀) = (0.5, 0.5, 0.5). (a) Government’s strategy x. (b) Residents’ strategy y. (c) Contractor’s strategy z. The specific values of e for each trajectory are 1.0, 1.5, 1.6, 1.7, and 1.8, as indicated in the legend. The X-axis, “Time (Simulation Steps)”, represents the iteration steps in the numerical simulation.

The simulation results for the cost-burden perception coefficient e (Figure 6) reveal the dominant role of residents’ subjective cognition in decision-making and its critical threshold effect. Marginal increases in e can sharply alter the system’s convergence, consistent with the loss-aversion principle in behavioral economics—residents attach much greater psychological weight to immediate cash outlays than to future asset appreciation. When e ≤ 1.7, objective economic returns still prevail, and the system converges to the desired state E₁(1,1,1). Once e > 1.7, subjective cost perception overwhelms objective benefit calculations; the residents’ strategy rapidly shifts to disengagement(y → 0), triggering a cascading breakdown of the cooperation network.

This critical phenomenon underscores the mental-accounting nature of residents’ decisions. Policy interventions cannot rely solely on optimizing objective economic parameters; they must also directly target the psychological cost account through financial instrument innovation (e.g., installment payment schemes, long-term low-interest loans) and communication strategies, thereby keeping the perceived burden e strictly below the threshold. This constitutes the most crucial micro-psychological pathway for overcoming the participation bottleneck.

4.7. Accident-Risk Perception Coefficient (d)

We sequentially set d to 0.0, 0.1, 0.2, 0.3, and 1.0 and obtain behavioral evolutionary simulations of how different accident-risk perception coefficients affect the three parties’ strategies, as shown in Figure 7: panel (a) presents the government’s behavioral evolution, panel (b) the residents’, and panel (c) the contractor’s.

Figure 7. Evolutionary trajectories of strategies under different d. The initial strategy proportions are (x_0, y_0, z₀) = (0.5, 0.5, 0.5). (a) Government’s strategy x. (b) Residents’ strategy y. (c) Contractor’s strategy z. The specific values of d for each trajectory are 0.0, 0.1, 0.2, 0.3, and 1.0, as indicated in the legend. The X-axis, “Time (Simulation Steps)”, represents the iteration steps in the numerical simulation.

The simulation results for the accident-risk perception coefficient d (Figure 7) reveal the limited efficacy and saturation pattern of risk communication in driving residents’ decisions. Increasing d effectively promotes residents’ participation in renewal, but its incentive effect exhibits diminishing marginal utility, consistent with protection-motivation theory in behavioral science. When d < 0.2, residents remain in a state of “risk neglect,” and the system falls into a “wait-and-see trap.” Once d ≥ 0.2 crosses the decision threshold, the residents’ strategy begins to shift toward active participation; however, when d > 0.3, the marginal incentive effect weakens markedly.

This nonlinear relationship provides a key policy insight: single-track risk warnings face a ceiling effect. A dual-engine mechanism of “risk early warning + economic incentives” is required. On the one hand, establish credible risk-communication channels through professional assessment and information transparency; on the other, pair them with concrete economic incentives that translate abstract risks into perceivable, near-term gains and losses. Only then can residents’ decision inertia be effectively overcome.

4.8. Sensitivity and Robustness Analysis (w,p,e)

To examine the interaction effects among multi-dimensional policy levers and the robustness of the system, this section conducts crossed simulations of the tripartite strategic evolutionary trajectories under controlled conditions. The resource-allocation lever (area-expansion coefficient w) is set to 0.34 and the cost-sharing lever (expansion-purchase coefficient p) is set to 0.71, while the resident cost-burden perception coefficient e is varied sequentially from 1.0, 1.5, 1.6, 1.7, to 1.8. The results are shown in Figure 8: panel (a) presents the government’s behavioral evolution, panel (b) the residents’, and panel (c) the contractor’s.

Figure 8. Evolutionary trajectories of strategies under w = 0.34, p = 0.71, and different e. The initial strategy proportions are (x_0, y_0, z₀) = (0.5, 0.5, 0.5). (a) Government’s strategy x. (b) Residents’ strategy y. (c) Contractor’s strategy z. The specific values of e for each trajectory are 1.0, 1.5, 1.6, 1.7, and 1.8, as indicated in the legend. The X-axis, “Time (Simulation Steps)”, represents the iteration steps in the numerical simulation.

The simulation results reveal that under the combined configuration of w and p specified above, the residents’ strategy y can still converge to active participation (y = 1) even when e = 1.8. This contrasts with the earlier single-parameter analysis (Section 4.6), where e > 1.7 led to resident withdrawal from cooperation. This finding indicates that the coordinated optimization of the resource-allocation lever (w) and the cost-sharing lever (p) can effectively raise the psychological tolerance threshold of residents towards the financial burden, thereby transforming a previously infeasible behavioral scenario into a feasible one. This result highlights significant complementary effects between different policy dimensions. It suggests that practical policy design should avoid relying on single instruments. Instead, a coordinated policy portfolio—characterized by a “high w–medium p–high e tolerance” combination—should be implemented to form a systematic incentive structure, thereby enhancing the overall robustness and adaptability of the policy.

5. Discussion

This study, via numerical simulations, uncovers the complex evolutionary dynamics of strategic behavior among the government, residents, and the contractor within the autonomous renewal system. Classified by functional dimension, the six key parameters can be consolidated into three categories of policy instruments, whose underlying mechanisms and policy implications are as follows.

5.1. Mechanisms of Key Parameters and Policy Implications

Through numerical simulations, this study systematically reveals the complex evolutionary dynamics of strategic behavior among the government, residents, and the contractor within the autonomous renewal system. Classified by their functional dimensions, the six key parameters can be consolidated into three categories of policy instruments; their underlying mechanisms and policy implications are as follows:

(1) Resource-allocation parameters (w,v) determine the macro-level incentive landscape. The floor-area expansion coefficient (w) is the core physical lever for mobilizing residents’ participation, but its effect follows an inverted-U pattern, requiring a balance between residents’ perceived gains and the government’s infrastructure carrying capacity. The expansion benefit-sharing coefficient (v) directly calibrates fiscal sustainability between the government and the contractor: if v is too low, the contractor is insufficiently incentivized; if v is too high, it erodes the government’s revenue base. This implies that the government should prioritize system-wide objectives over marginal fiscal returns, using moderate benefit-sharing concessions to crowd in market participation. Together, these two parameters constitute the macro-level driving framework for project initiation.

(2) Cost-sharing parameters (p,q) operate at the micro-transactional level to finely calibrate residents’ out-of-pocket pressure. The expansion-purchase coefficient (p)—the government’s pricing-control instrument—and the Original-Area Reconstruction Payment Coefficient (q)—the contractor’s commercial price-concession instrument—exhibit pronounced policy complementarity. In practice, the government can signal fiscal forbearance by setting a relatively low p (e.g., 0.7–0.8) while, through mechanisms, such as a contractor reputation evaluation system, incentivizing the contractor to offer moderate q concessions (≥0.5). This combined approach of government tax relief and contractor price concessions effectively lowers residents’ effective participation threshold.

(3) Behavioral-intervention parameters (e,d) reveal the psychological pathways for overcoming residents’ decision barriers. The critical threshold effect of the cost-burden perception coefficient (e) underscores the paramount importance of alleviating residents’ immediate payment pressure. Policy should prioritize financial-instrument innovation, such as providing long-term low-interest loans or establishing a “Renewal Fund” to enable installment payments. By contrast, the saturation effect of the accident-risk perception coefficient (d) indicates diminishing returns to risk communication once the threshold is reached. Consequently, public policy should move beyond warning-only approaches and construct a dual-engine mechanism of “risk early warning + economic incentives” that, leveraging objective data and representative cases, translates abstract risks into perceivable future payoff losses.

5.2. Systemic Coordination of the Parameter System and Pathways to Resolving the E₃ Dilemma

The most important finding of this study is that the six key parameters driving the autonomous renewal system constitute a tightly coupled, mutually constraining organic whole. The effectiveness of adjusting any single parameter is highly contingent on the coordination state of the others; this intrinsic interdependence is especially salient when attempting to overcome the common E₃(1,0,1) dilemma. At its core, this dilemma persists because residents’ objective cost thresholds and subjective perception barriers have not been effectively dismantled. Achieving the pivotal transition to the desired state E₁(1,1,1) requires systems thinking and the implementation of a precisely calibrated policy mix.

Specifically, increasing the floor-area expansion coefficient w in isolation—without a concurrent reduction in the expansion-purchase coefficient p or an increase in the Original-Area Reconstruction Payment Coefficient q—will see the residents’ objective gains offset by higher out-of-pocket contributions, thereby failing to generate an effective incentive. Accordingly, a linked regime of “high-w–medium-p–high-q” should be established to jointly calibrate residents’ effective costs while preserving the baseline returns of the government and the contractor. More critically, targeted intervention on the cost-burden perception coefficient e is needed: introduce financial instruments such as long-term low-interest loans and installment-payment schemes to convert large one-off expenditures into smaller, long-horizon payments, thereby directly reducing residents’ perceived cost burden.

Advancing this transition requires a phased, dynamic strategy. In the initiation phase, policy should prioritize reducing perceived burden (managing e) and heightening risk awareness (activating d), rapidly shifting residents’ decision calculus through robust risk communication and targeted financial support. In the consolidation phase, once residents’ willingness has been initially catalyzed, the focus should pivot to stabilizing the cost-sharing levers (locking in p and q) and the resource-allocation lever (maintaining v), thereby ensuring the sustainability of the contractor’s participation incentives and preventing regression to the E3(1,0,1) state.

This dynamic adjustment strategy must be tightly tailored to community contexts, acknowledging socioeconomic heterogeneity. In low-income communities, where upfront payment capacity is the primary constraint, the policy mix should markedly increase the weight of cost-sharing and behavioral-intervention levers. This could involve setting a significantly lower expansion-purchase coefficient (e.g., p ≈ 0.6), combined with substantial government subsidies and accessible long-term, low-interest loan products to directly alleviate the financial burden and lower the effective e. Conversely, in higher-income communities where affordability is less of an issue but “wait-and-see” inertia may prevail, policy can place relatively more emphasis on optimizing the resource-allocation levers (notably w and v) and, crucially, on implementing intensive risk communication campaigns (e.g., through professional safety assessments and VR hazard simulations) to elevate the accident-risk perception coefficient d to a decision-salient level.

To translate the analytical findings into actionable strategies, Table 6 provides a concrete mapping between the multi-dimensional policy levers and specific, implementable policy instruments. This portfolio allows policymakers to mix and match tools from different dimensions to form a synergistic strategy tailored to local contexts.

Table 6. Mapping multi-dimensional policy levers to concrete policy instruments.

Policy Lever Dimension	Core Parameter	Concrete Policy Instruments
Resource-Allocation Levers	w	• Granting FAR (Floor Area Ratio) bonuses • Transfer of Development Rights (TDR)
	v	• Public-private partnership (PPP) agreements • Land concession agreements with profit-sharing clauses
Cost-Sharing Levers	p	• Direct housing price subsidies for the expanded area • Capping the purchase price of new floor area below market rate
	q	• Mandating or incentivizing contractors to offer “cost-price” or discounted reconstruction packages • Government-negotiated bulk discount rates for residents
Behavioral-Intervention Levers	e	• Financial Innovation: Establishing a dedicated “Renewal Loan” product (e.g., featuring a 20% down-payment and a 3% annual interest rate) to convert large one-time payments into manageable installments • Mental Accounting: Framing the investment as a “home value appreciation fund” rather than a pure cost
	d	Risk Communication: • VR Hazard Visualization: Using virtual reality to simulate fire, earthquake, or structural failure scenarios in aging buildings • Mandatory Safety Drills: Organizing community-wide emergency evacuation exercises • Transparent Risk Reporting: Publicly sharing official structural safety assessment reports

6. Conclusions

This study constructs a government–residents–contractor tripartite evolutionary game model and, innovatively, introduces a Multi-dimensional Policy-Lever System analytical framework to systematically elucidate the complex driving mechanisms of autonomous renewal in China’s aging urban communities. The core finding indicates that successfully advancing original-area reconstruction does not hinge on a single, forceful policy intervention; rather, it requires a finely balanced, synergistic parameter system that steers the strategies of all three parties toward a cooperative equilibrium.

At the theoretical level, the main contributions of this study are as follows: First, it transcends the traditional homo economicus assumption by quantifying the cost-burden perception coefficient (e) and the accident-risk perception coefficient (d), thereby systematically embedding a behavioral-science perspective into evolutionary game analysis and providing a key micro-psychological explanation of the “policy-hot, residents-cold” phenomenon. Second, the proposed Multi-dimensional Policy-Lever System integrates three classes of instruments—resource allocation (w,v), cost sharing (p,q), and behavioral intervention (e,d)—offering a unified theoretical framework and analytical paradigm to address the fragmentation of policy tools in renewal practice.

At the practice and policy levels, this study offers a clear control pathway and quantitative reference points for designing targeted renewal policies. The simulation results indicate that the resource-allocation levers (w,v) exhibit an inverted-U effect with dual threshold effects; the cost-sharing levers (p,q) must locate a critical balance point between incentivizing residents and maintaining the project’s economic feasibility; and the behavioral-intervention levers (e,d) feature distinct perceptual thresholds and saturation effects. Accordingly, policy design should shift from unidirectional incentivization to coordinated co-regulation, leveraging dynamic, portfolio-based policy instruments to simultaneously enhance the environmental efficiency, economic feasibility, and social equity of community renewal—thereby providing a practicable governance pathway that directly supports United Nations Sustainable Development Goal (SDG 11): making cities and human settlements inclusive, safe, resilient, and sustainable [78].

This study nonetheless has limitations that point to fruitful directions for future research. First, the generalizability of the model parameters, primarily calibrated based on the representative case of Hangzhou, awaits further validation across a broader set of cases from diverse socioeconomic and regional contexts. Future research can be deepened by conducting cross-regional comparative studies to verify the model’s applicability and identify context-specific heterogeneities. Second, the current model does not incorporate spatial spill-over effects, such as the imitation behaviors among residents in adjacent communities or the impact of one regeneration project on the property values and renewal decisions in surrounding neighborhoods. Incorporating temporal dynamics and spatial heterogeneity into the modeling framework would enhance its capacity to simulate more complex real-world systems. Future models could also incorporate more sophisticated contractual arrangements, such as savings-sharing mechanisms from EPC projects, to further refine the representation of contractor incentives. Third, future research could incorporate more formal behavioral specifications, such as a full Prospect Theory value function and Prelec probability-weighting function, to achieve even finer granularity in capturing residents’ risk decision-making processes. Fourth, future research can enhance analytical framework by implementing more formal behavioral specifications, such as a full Cumulative Prospect Theory framework with value and probability-weighting functions, to achieve even greater precision in characterizing agents’ risk-sensitive decision-making. Fifth, future models could explore the implementation of formal normalization coefficients or dimensionless scaling to refine the aggregation of monetary and non-monetary payoff components. Furthermore, future work could employ advanced global sensitivity analysis techniques, such as the Sobol’ method, to further quantify the influence of each parameter under a wider range of uncertainties.