Games

27 pages, 2148 KB

Open AccessArticle

Endogenous Agreement Geometry in Nash Bargaining over a Continuum of Issues

by Alessio Staffini

Games 2026, 17(4), 41; https://doi.org/10.3390/g17040041 - 6 Aug 2026

Many bargaining problems allocate control over heterogeneous issues rather than a single scalar surplus. This paper studies a two-player game-theoretic Nash bargaining problem over a continuum of issues with stochastic valuation fields. Taking the classical maximum Nash welfare cutoff allocation as a benchmark, [...] Read more.

Many bargaining problems allocate control over heterogeneous issues rather than a single scalar surplus. This paper studies a two-player game-theoretic Nash bargaining problem over a continuum of issues with stochastic valuation fields. Taking the classical maximum Nash welfare cutoff allocation as a benchmark, we characterize the selected agreement as an endogenous excursion set of the log-relative valuation field. We then study its economic geometry: stationarity and ergodicity yield deterministic many-issue payoff limits, a finite-domain perturbation formula separates local shocks from global cutoff feedback, Kac–Rice methods describe boundary intensity, and a perimeter penalty for fragmented contracts turns the bargain into a finite perimeter variational problem. At regular boundary points, the complexity-penalized bargain satisfies a curvature-adjusted bargaining condition. The analysis connects cooperative game theory, Nash bargaining, fair division, random field geometry, and contract complexity. Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

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21 pages, 384 KB

Open AccessFeature PaperArticle

Credence Goods in Markets with Collective Reputation: Nature of Equilibria and the Value of Certification

by Erin Krupka, Thomas P. Lyon and Arnab Mitra

Games 2026, 17(4), 40; https://doi.org/10.3390/g17040040 - 24 Jul 2026

Abstract

Fraud can cause markets for credence goods to collapse, but collective reputation has been suggested as a potential solution, especially when buyer valuations for quality are high. We develop a discrete model of a market for label credence goods and provide conditions for [...] Read more.

Fraud can cause markets for credence goods to collapse, but collective reputation has been suggested as a potential solution, especially when buyer valuations for quality are high. We develop a discrete model of a market for label credence goods and provide conditions for no-fraud equilibria based on collective reputation. We identify conditions under which all equilibria may be asymmetric or involve mixed strategies and hence sellers may face coordination problems. Our analysis suggests such coordination problems are the greatest when the size of the high-quality market is approximately half of the overall market (that incorporates both high- and low-quality goods), in the absence of any focal point or coordination device. Concerning certification, we find that it may not be particularly useful when buyer valuations for credence attributes are high under a well-performing collective reputation regime and a relatively small-sized low-quality market. However, we also determine that certification may serve its purpose the most when buyer valuations for credence attributes are low (contrary to standard intuition) and/or the size of the high-quality market is around half of the overall market (i.e., the high- and low-quality markets are of approximately equal size). Finally, our results indirectly indicate that agencies/NGOs concerned about fraudulent behavior may focus their attention on markets where heterogenous firms enjoy collective reputation. Full article

(This article belongs to the Section Applied Game Theory)

18 pages, 5336 KB

Open AccessFeature PaperArticle

Inefficient Learning Leads to Efficient Coordination: A Repeated Stag-Hunt Game with Learning Agents

by Ren Manfredi, Daniele Vilone, Tijan J. Cvetkovic, Franco Bagnoli and Andrea Guazzini

Games 2026, 17(4), 39; https://doi.org/10.3390/g17040039 - 23 Jul 2026

Abstract

In coordination games, the distinctive presence of multiple equilibria poses a challenge to coordination, and this has led over time to the proposal of numerous determinants of the latter. In this paper, we study coordination in a repeated Stag-hunt game played by two [...] Read more.

In coordination games, the distinctive presence of multiple equilibria poses a challenge to coordination, and this has led over time to the proposal of numerous determinants of the latter. In this paper, we study coordination in a repeated Stag-hunt game played by two agents who are able to learn from the outcomes of each game, but do not know the payoff matrix. By modulating their learning capabilities, we show that agents are able to coordinate on the social optimum when they learn slowly from experience and are prone to making mistakes. A comparison with the results from a recent laboratory experiment is also provided. Full article

(This article belongs to the Section Learning and Evolution in Games)

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43 pages, 961 KB

Open AccessFeature PaperArticle

Promotion Thresholds, Revenue Sharing, and Delivery Risk in Reward-Based Crowdfunding

by Joyaditya Laik, Esther Gal-Or and Prakash Mirchandani

Games 2026, 17(4), 38; https://doi.org/10.3390/g17040038 - 21 Jul 2026

Abstract

This paper investigates two marketing strategies a reward-based crowdfunding platform employs to align its preferences with an entrepreneur’s choice of pledge and target levels. These are (a) how to promote campaigns to potential backers, and (b) how to share campaign revenues with the [...] Read more.

This paper investigates two marketing strategies a reward-based crowdfunding platform employs to align its preferences with an entrepreneur’s choice of pledge and target levels. These are (a) how to promote campaigns to potential backers, and (b) how to share campaign revenues with the entrepreneur. Kickstarter, for instance, promotes a set of campaigns by compiling a list of “recommended” projects. This research shows that the platform’s choice of the promotion rule may expose entrepreneurs to the risk of not generating sufficient funds to start production, which can damage their and the platform’s reputation. When the platform’s reputational risk is not very high, it reduces the risk of non-delivery by increasing the revenue share of the entrepreneur. The platform’s strategies are likely to ensure production when backers derive warm glow from pledging, when the entrepreneur’s development cost is low, or when the entrepreneur has minimal reputational cost if production fails. However, low reputational costs motivate the entrepreneur to lower the target, thus increasing the likelihood of insufficient funds to start production. We propose strategies the platform can use, including customizing the revenue share based on the campaign characteristics, to rectify such misalignments. Full article

(This article belongs to the Section Applied Game Theory)

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39 pages, 1516 KB

Open AccessFeature PaperArticle

Decentralized, Efficient, and Fair: Mean-Field Predictive Control for Bidirectional EV Coordination Under Uncertainty

by Samuel M. Muhindo

Games 2026, 17(4), 37; https://doi.org/10.3390/g17040037 - 9 Jul 2026

Abstract

We propose a decentralized strategy for coordinating the bidirectional charging and discharging of battery electric vehicles (BEVs) in renewable-powered parking lots. The framework combines mean-field games (MFGs) and model predictive control (MPC) to address the coupled stochastic dynamics induced by uncertain renewable generation [...] Read more.

We propose a decentralized strategy for coordinating the bidirectional charging and discharging of battery electric vehicles (BEVs) in renewable-powered parking lots. The framework combines mean-field games (MFGs) and model predictive control (MPC) to address the coupled stochastic dynamics induced by uncertain renewable generation and random vehicle arrivals and departures. Solar and wind power fluctuations are modeled using autoregressive moving-average (ARMA) processes, while the time-varying vehicle population is represented through finite Poisson processes. The coordination problem is formulated as a large-scale game, where an aggregator designs individual cost functions to maximize available energy utilization while promoting fairness through near-equal states of charge (SOCs) at departure. Scalability is achieved through MFG theory, ensuring convergence and stability even under highly volatile generation and fluctuating agent populations. Numerical simulations validate the proposed strategy against two straightforward algorithms: capacity-ordered saturation allocation (COSA) and capacity-ordered fair allocation (COFA). These centralized approaches achieve high target fulfillment in static, low-intensity environments, where available energy accommodates a stable fleet without exceeding power limits. However, their efficacy degrades significantly in dynamic, high-intensity environments, where the interplay of volatile generation, continuous fleet turnover, and strict power constraints strains the system. In contrast, the proposed MFG-MPC framework provides a decentralized response that elegantly navigates the trade-offs between energy availability, demand stochasticity, and power limits. Ultimately, this approach ensures robust energy utilization while safeguarding vehicle equity, confirming its strong suitability for real-time deployment. Full article

(This article belongs to the Special Issue Dynamic Game Theory in Sustainability)

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34 pages, 6647 KB

Open AccessArticle

Engineered Misunderstanding Under Psychological Warfare: A Bayesian Signaling Game of Felt-Understanding Collapse in the German Atomausstieg

by Ryanne R. L. Fairchild

Games 2026, 17(4), 36; https://doi.org/10.3390/g17040036 - 2 Jul 2026

Abstract

Russian state-sponsored disinformation has been described in policy and the operational literature, but it is less often formalized in game-theoretic terms. Here, a two-layered formal model is developed showing how adversarial perturbation of a communication channel can collapse cross-group felt understanding—the third-order intentional [...] Read more.

Russian state-sponsored disinformation has been described in policy and the operational literature, but it is less often formalized in game-theoretic terms. Here, a two-layered formal model is developed showing how adversarial perturbation of a communication channel can collapse cross-group felt understanding—the third-order intentional state/belief structure, established empirically by Livingstone, in which one group believes its perspectives are recognized and accepted as valid by another. The Analytical Model is a static Bayesian signaling game with binary types and a noisy channel parameterized by perturbation rate π. The Analytical Model shows that when recognition benefits exceed signaling costs, there exists a perturbation threshold π* = 1 − c_R/(u_R · p) above which mutual misrecognition becomes the unique Perfect Bayesian Equilibrium outcome. The Computational Model embeds this logic in an agent-based simulation on a homophilic stochastic block model and scale-free networks with continuous recognition capacity. Four substantive findings emerge: the closed-form analytical threshold from the Analytical Model predicts the boundary of collapse in the dynamic networked simulation; high network homophily protects cooperative behavior below π* but provides no rescue above it; bridge seeding—the placement of recognition-capable agents at structurally central cross-group positions—is the most effective of three policy interventions tested, rescuing cooperation even above π*; and uniform adversarial volume is approximately as damaging as strategically targeted adversarial precision across both small dense and large scale-free topologies, qualifying the operational claim that targeted disinformation should strictly outperform volume-based approaches. The model is illustrated with the German Atomausstieg (nuclear phase-out) case, and implications for clinical psychology, public policy, and intergroup recognition under psychological warfare are discussed. Full article

(This article belongs to the Special Issue Games with Incomplete Information)

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Graphical abstract

15 pages, 300 KB

Open AccessArticle

Fixed-Time Pursuit–Evasion Differential Game with Grönwall Constraints in Hilbert Space l₂

by Gafurjan Ibragimov, Saidakbar Gulomov and Bruno Antonio Pansera

Games 2026, 17(4), 35; https://doi.org/10.3390/g17040035 - 2 Jul 2026

Abstract

This paper studies a pursuit–evasion differential game in the Hilbert space

l_{2}

involving countably many pursuers and one evader. The players follow simple motion dynamics, while their control functions are subject to Grönwall-type constraints. The value of the game

λ

is defined [...] Read more.

This paper studies a pursuit–evasion differential game in the Hilbert space

l_{2}

involving countably many pursuers and one evader. The players follow simple motion dynamics, while their control functions are subject to Grönwall-type constraints. The value of the game

λ

is defined as the infimum of the distances between the evader and the pursuers at a given terminal time

θ

. The pursuers aim to minimize this distance

λ

by the end of the game, while the evader aims to keep it as large as possible. Optimal strategies for the pursuers are constructed via the method of fictitious pursuers, and an explicit evasion strategy is derived. As a result, the optimal strategies of both sides and the value of the game are obtained. Full article

22 pages, 1776 KB

Open AccessFeature PaperArticle

Markovian Analysis of a Small Population Evolutionary Prisoner’s Dilemma Game

by Athanasios Kehagias

Games 2026, 17(4), 34; https://doi.org/10.3390/g17040034 - 25 Jun 2026

Abstract

In this work we consider an evolutionary game in which a small population repeatedly plays the Iterated Prisoner’s Dilemma (IPD) game using the pairwise proportional imitation (PPI) revision protocol. Since we are dealing with a small population, we can explicitly formulate a Markov [...] Read more.

In this work we consider an evolutionary game in which a small population repeatedly plays the Iterated Prisoner’s Dilemma (IPD) game using the pairwise proportional imitation (PPI) revision protocol. Since we are dealing with a small population, we can explicitly formulate a Markov chain (MC) model of the evolutionary game and study its properties. In particular, we identify the absorbing states and their basins of attraction. In addition, we briefly study the replicator dynamics of the same game for the case of a large population. We find that, as the size of the population increases, the Markovian dynamics approximate the replicator dynamics. Full article

(This article belongs to the Special Issue Evolutionary Games on Networks and Biological Systems)

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18 pages, 3860 KB

Open AccessArticle

Politically Dangerous Minds: A Game-Theoretic Analysis of Vygotsky, Luria, and the Socially Mediated Survival of Knowledge

by Ryanne R. L. Fairchild

Games 2026, 17(3), 33; https://doi.org/10.3390/g17030033 - 22 Jun 2026

Abstract

Scientific theories survive on institutional fitness, not empirical merit alone. Under Soviet Stalinism, Vygotsky and Luria’s cultural-historical psychology was suppressed while Leontiev’s Activity Theory flourished because it aligned with Marxist-Pavlovian materialism. A game-theoretic framework formalizes this dynamic through three coupled mechanisms: a researcher [...] Read more.

Scientific theories survive on institutional fitness, not empirical merit alone. Under Soviet Stalinism, Vygotsky and Luria’s cultural-historical psychology was suppressed while Leontiev’s Activity Theory flourished because it aligned with Marxist-Pavlovian materialism. A game-theoretic framework formalizes this dynamic through three coupled mechanisms: a researcher utility function (U_r = αT + βR − γC), a state utility function (U_s(e) = δI(e) − εD(e) − κ(e)), and a replicator dynamic for institutional selection. Under sufficiently high punishment coefficients, the unique Nash equilibrium is aligned with the ideologically safe theory regardless of empirical truth, and the replicator dynamics drive empirically stronger theories to extinction in the institutional population. Classical findings on conformity and obedience from Sherif, Asch, Festinger, Schachter, and Milgram supply the foundations for the model’s parameters. This pattern—termed here as epistemological selection pressure—explains the Vygotsky case. Because the model assumes severe punishment, active enforcement, complete information, and a binary choice, it applies most directly to authoritarian science; contemporary liberal institutions correspond to the low-punishment regime in which the same model predicts that empirical merit can prevail, so the mechanism is expected to recur only in attenuated form within specific high-pressure domains where scientific truth and institutional power remain entangled. Full article

(This article belongs to the Section Applied Game Theory)

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12 pages, 727 KB

Open AccessArticle

Relative Consumption as Fitness: A Replicator–Mutator Model of Reference-Dependent Demand and Status Competition

by Aras Yolusever

Games 2026, 17(3), 32; https://doi.org/10.3390/g17030032 - 18 Jun 2026

Abstract

Background: Standard consumer theory treats preferences as fixed primitives and demand as the solution to an individual optimisation problem; we instead model consumption styles as heritable strategies whose prevalence is shaped by selection and experimentation, and ask when status competition produces an [...] Read more.

Background: Standard consumer theory treats preferences as fixed primitives and demand as the solution to an individual optimisation problem; we instead model consumption styles as heritable strategies whose prevalence is shaped by selection and experimentation, and ask when status competition produces an over-consumption trap. Methods: We embed a reference-dependent payoff—private utility concave in own consumption, a positional benefit proportional to consumption relative to the social mean, a financial-fragility cost, and a loss-averse relative-deprivation term—into replicator–mutator dynamics over three strategies (frugal, balanced, conspicuous). Results: Status concern induces strategic complementarity, so that a rising consumption norm penalises moderate consumers and makes imitation self-reinforcing. For intermediate status weight, the system is bistable: an efficient balanced equilibrium and a Pareto-inferior conspicuous trap are separated by a tipping threshold, and the width of the bistable window equals the deprivation weight, producing hysteresis in the consumption norm. The trap persists even though the positional benefit nets to zero in any monomorphic state. Mutation—behavioural experimentation—shrinks the bistable window and can dissolve the lock-in. Conclusions: Reference-dependent demand is better captured by evolutionary dynamics than by static equilibrium, and positional externalities can lock a population into self-defeating over-consumption that interventions on the deprivation or fragility channel may unlock. Full article

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34 pages, 532 KB

Open AccessArticle

The Effect of Competition on Dishonesty, Trade, and Consumer Trust

by Silvia Martinez-Gorricho

Games 2026, 17(3), 31; https://doi.org/10.3390/g17030031 - 17 Jun 2026

Abstract

This paper considers a multi-period two-sided asymmetric information model with infinitely long-lived sellers and short-lived buyers. I assume that two exogenously given qualities are offered in the market. Each period, a consumer, who is uncertain about the quality of the offered product, observes [...] Read more.

This paper considers a multi-period two-sided asymmetric information model with infinitely long-lived sellers and short-lived buyers. I assume that two exogenously given qualities are offered in the market. Each period, a consumer, who is uncertain about the quality of the offered product, observes her pairwise matched seller’s price and a noisy signal of quality that cannot be manipulated by the seller. Prices are fixed and it is common knowledge that consumers are not willing to pay a high price for the low-quality product. A matched seller with a low-quality good can choose to be either honest (by charging the lower market price) or dishonest (by charging the higher price). Sellers’ incentives to misrepresent quality depend on how current trade outcomes affect future access to consumer traffic. I show that the strength of the informational role of prices is non-decreasing in the intensity of competition for future consumer traffic in equilibrium and that consumers do not benefit from more intense competition. Full article

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21 pages, 1519 KB

Open AccessArticle

The Relationships Between Oil, Critical Minerals, and Military Expenditure: Evidence from the U.S. and China

by Luccas Assis Attílio, Joao Ricardo Faria, Mauro Rodrigues and Emilson Silva

Games 2026, 17(3), 30; https://doi.org/10.3390/g17030030 - 16 Jun 2026

Abstract

This paper investigates the interplay between oil, critical minerals, and military expenditure in the U.S. and China. The research goal is to evaluate how sensitive the military expenditure of these countries is to shocks in energy markets. It develops a stylized dynamic model [...] Read more.

This paper investigates the interplay between oil, critical minerals, and military expenditure in the U.S. and China. The research goal is to evaluate how sensitive the military expenditure of these countries is to shocks in energy markets. It develops a stylized dynamic model of the arms race and conflict, with a particular focus on U.S.–China tensions surrounding access to these vital resources. Empirical analysis using VAR estimations reveals that: (1) shocks to China’s military spending prompt increases in U.S. military expenditure, whereas the reverse effect is not observed; (2) critical mineral production significantly influences China’s military spending; and (3) U.S. military expenditure is affected by both Chinese military spending and fluctuations in oil prices. Full article

(This article belongs to the Special Issue Economic Theory and Applications)

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20 pages, 458 KB

Open AccessFeature PaperArticle

A Provable Semi-Infinite Programming Approach for Solving Constrained Dynamic Games

by Tyler C. Gardner, Matthew W. Harris and Logan Lancaster

Games 2026, 17(3), 29; https://doi.org/10.3390/g17030029 - 3 Jun 2026

Abstract

Many engineering problems must account for the non-cooperative decisions and actions of multiple players. These problems can be modeled within a game-theoretic framework. The approach herein is to model such problems as mathematical games, convert them to semi-infinite programs, and utilize a semi-infinite [...] Read more.

Many engineering problems must account for the non-cooperative decisions and actions of multiple players. These problems can be modeled within a game-theoretic framework. The approach herein is to model such problems as mathematical games, convert them to semi-infinite programs, and utilize a semi-infinite program solver whose output is provably an

ϵ

-optimal Nash equilibrium. The approach is successfully benchmarked on two low-dimensional problems. Two types of higher-dimensional linear quadratic dynamic games are then investigated: ones where each player’s problem is convex and ones where at least one player’s problem is nonconvex. Within each type, variations based on information structure, control constraints, number of players, and semi-infinite objective are considered. The algorithm is tested with different internal solvers, and it successfully solves all test problems using MATLAB’s fmincon. The numerical solutions approximate analytical solutions (when they are known) within approximately one percent. For a three-player game with input saturation constraints, hundreds of variables, and no analytical solution, the computational time is approximately five minutes. Full article

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17 pages, 519 KB

Open AccessArticle

A Cooperative Pollution Control Differential Game with Randomly Switching Payoffs

by Feiran Xu and Anna Tur

Games 2026, 17(3), 28; https://doi.org/10.3390/g17030028 - 29 May 2026

Abstract

We study a continuous-time cooperative differential game of pollution control in which the pollution stock accumulates emissions and affects long-run welfare. The key feature is a one-time random increase in the public damage weight, interpreted as a regime shift in environmental policy, social [...] Read more.

We study a continuous-time cooperative differential game of pollution control in which the pollution stock accumulates emissions and affects long-run welfare. The key feature is a one-time random increase in the public damage weight, interpreted as a regime shift in environmental policy, social damage assessment, or regulatory pressure. Using dynamic programming, we characterize the grand-coalition feedback solution from the Hamilton–Jacobi–Bellman equations and derive closed-form expressions for cooperative emissions, pollution dynamics, regime-specific steady states, and transition paths. Under emission caps, we construct the coalition characteristic function using a conservative worst-case benchmark for outsider behavior rather than an unlimited-pollution assumption. For payoff allocation, we derive a dynamic payment schedule that implements the Shapley allocation along the stochastic pollution path and keeps the remaining payoff consistent with the corresponding continuation game. Finally, we extend the framework to a threshold-triggered shifted-exponential switching mechanism. This extension gives a computable objective for the optimal threshold-hitting time and clarifies how the pollution threshold and switching hazard can be interpreted as policy-relevant indicators of regulatory or ecological regime change. Full article

(This article belongs to the Section Cooperative Game Theory and Bargaining)

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24 pages, 1171 KB

Open AccessArticle

When Context Shapes Preferences: Norm Erosion and Context-Dependent Fairness Concerns in Public Goods Games

by Chanalak Chaisrilak and Thanee Chaiwat

Games 2026, 17(3), 27; https://doi.org/10.3390/g17030027 - 26 May 2026

Abstract

Public goods provision is vulnerable to free riding, making sustained cooperation a central challenge in economics. Fehr and Schmidt’s inequity-aversion model explains how fairness concerns can support cooperation, but it treats preferences as fixed. Motivated by Kimbrough and Vostroknutov’s norm-sensitivity framework, this paper [...] Read more.

Public goods provision is vulnerable to free riding, making sustained cooperation a central challenge in economics. Fehr and Schmidt’s inequity-aversion model explains how fairness concerns can support cooperation, but it treats preferences as fixed. Motivated by Kimbrough and Vostroknutov’s norm-sensitivity framework, this paper develops a reduced-form dynamic framework in which observed norm violations erode normative commitment over time. As normative commitment declines, the model maps this change into Fehr–Schmidt-style fairness parameters: guilt weakens and envy rises. These parameters provide an interpretive representation of norm erosion, while behavior is generated through a tractable contribution-scaling rule. The framework is calibrated illustratively to the public goods experiment of Fischbacher and Gächter. The calibration is not causal evidence of preference change and does not directly identify inequity-aversion parameters. It shows that a context-dependent preference channel can reproduce the observed aggregate decline in cooperation and generate testable implications. When no free-rider exposure is present, cooperation does not decline within the model. The model also predicts a nonlinear relationship between population-level free-rider prevalence and cooperation. Finally, because the model imposes a lower bound on normative commitment, this institutional floor determines long-run cooperation. The findings should be interpreted as model-based hypotheses for future experimental and field research. Full article

(This article belongs to the Section Behavioral and Experimental Game Theory)

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25 pages, 5327 KB

Open AccessArticle

Diffusion Mechanism of Regional Collaborative Strategy in Public Health Emergencies Considering Vertical Intervention

by Xiaoli Li and Luo Wu

Games 2026, 17(3), 26; https://doi.org/10.3390/g17030026 - 25 May 2026

Abstract

Frequent occurrences of inter-regional emergencies constitute critical impediments to global security and sustainable development, necessitating enhanced intergovernmental emergency collaboration. This study employs a network evolutionary game model (NEGM) to examine how vertical interventions shape diffusion mechanisms of cooperative strategies among local governments. The [...] Read more.

Frequent occurrences of inter-regional emergencies constitute critical impediments to global security and sustainable development, necessitating enhanced intergovernmental emergency collaboration. This study employs a network evolutionary game model (NEGM) to examine how vertical interventions shape diffusion mechanisms of cooperative strategies among local governments. The results show that (1) solely intensifying penalties or rewards yields diminishing marginal returns in incentivizing local governments to adopt a proactive cooperative strategy; (2) elevating the cost-sharing index significantly accelerates the diffusion rate of cooperative strategies, effectively mobilizing broader subnational engagement in public health emergency response; and (3) the tripartite integration of penalty-based enforcement, reward incentives, and cost-sharing mechanisms demonstrates synergistic superiority over alternative policy instruments—whether implemented individually or in pairwise combinations. Full article

(This article belongs to the Special Issue Advancements in Social Choice and Mechanism Design)

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17 pages, 295 KB

Open AccessFeature PaperArticle

Search Costs, Hassle Costs, and Drip Pricing: Equilibria with Rational Consumers and Firms

by Michael R. Baye and John Morgan

Games 2026, 17(3), 25; https://doi.org/10.3390/g17030025 - 21 May 2026

Abstract

This paper examines drip pricing related to compulsory charges—a situation where firms intentionally make it costly for consumers to discover mandatory fees or surcharges that “drip” into the full (total) price, which is only revealed after incurring the hassle cost of completing a [...] Read more.

This paper examines drip pricing related to compulsory charges—a situation where firms intentionally make it costly for consumers to discover mandatory fees or surcharges that “drip” into the full (total) price, which is only revealed after incurring the hassle cost of completing a purchase. We show that drip pricing can arise as an equilibrium phenomenon with fully rational consumers and profit-maximizing firms. We also show that when consumers and firms are rational (a) situations where drip pricing raises prices and harms consumers are unlikely to arise from unilateral business decisions and (b) the most likely avenue by which drip pricing harms consumers is through the coordinated adoption of drip pricing. Full article

(This article belongs to the Special Issue Economic Theory and Applications)

14 pages, 1089 KB

Open AccessArticle

Nonlinear Dynamics of Evolutionary Public Goods Games with Consistent- and Inconsistent-Moral-Standard Exclusive Sanctions

by Yang Chen and Xiaofeng Wang

Games 2026, 17(3), 24; https://doi.org/10.3390/g17030024 - 18 May 2026

Abstract

This paper investigates the evolution of public cooperation within a four-strategy public goods game that incorporates both consistently and inconsistently moralistic exclusion mechanisms. Using replicator dynamics in an infinite well-mixed population, we demonstrate that the presence of Inconsistent Moralists (IMs), i.e., non-contributors who [...] Read more.

This paper investigates the evolution of public cooperation within a four-strategy public goods game that incorporates both consistently and inconsistently moralistic exclusion mechanisms. Using replicator dynamics in an infinite well-mixed population, we demonstrate that the presence of Inconsistent Moralists (IMs), i.e., non-contributors who hypocritically exclude other defectors, fundamentally reshapes the dynamical structure of the multi-player social dilemma game. While the system admits no interior fixed point and the IM strategy itself is evolutionarily unstable, IM acts as a critical catalyst by destabilizing pure defection and redirecting evolutionary trajectories toward exclusion-based cooperation. Ultimately, these findings reveal that diverse enforcement strategies can qualitatively alter evolutionary outcomes by providing a previously overlooked indirect pathway for cooperation to emerge and persist in social dilemmas. Full article

(This article belongs to the Section Learning and Evolution in Games)

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18 pages, 1528 KB

Open AccessArticle

A Dynamic Game Model to Estimate Market Competitiveness: An Application to the Chinese Retail Oil Market

by Ying Zheng, Jiayi Xu and Xiao-Bing Zhang

Games 2026, 17(3), 23; https://doi.org/10.3390/g17030023 - 30 Apr 2026

Abstract

This paper develops a dynamic game-theoretic model to evaluate market competitiveness in industries characterized by price competition and adjustment stickiness. We extend the dynamic oligopoly framework for estimating market competitiveness in the literature from a quantity-setting to a price-setting context with differentiated goods. [...] Read more.

This paper develops a dynamic game-theoretic model to evaluate market competitiveness in industries characterized by price competition and adjustment stickiness. We extend the dynamic oligopoly framework for estimating market competitiveness in the literature from a quantity-setting to a price-setting context with differentiated goods. By deriving the subgame perfect equilibrium in a linear-quadratic structure, we utilize an index analogous to the price conjectural variation to measure market competitiveness with differentiated goods. The model is applied to the Chinese retail oil market, and we find that the Chinese retail oil market, particularly dominated by two state firms, exhibits characteristics close to a collusive benchmark within the maintained model. The dynamic game model provides a tractable analytical tool for antitrust authorities to monitor strategic coordination in dynamic environments where price transparency or regulation may facilitate tacit coordination of pricing behavior to a high degree. Full article

(This article belongs to the Section Applied Game Theory)

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