When Incentives Feel Different: A Prospect-Theoretic Approach to Ethereum’s Incentive Mechanism

Abstract

This study asks whether Ethereum’s proof-of-stake (PoS) incentives not only make economic sense on paper but also feel attractive to real validators who may be loss-averse and sensitive to risk. We take a canonical Eth2 slot-level model of rewards, penalties, costs, and proposer-conditional maximal extractable value (MEV) and overlay a prospect-theoretic valuation that captures reference dependence, loss aversion, diminishing sensitivity, and probability weighting. This Prospect-Theoretic Incentive Mechanism (PT-IM) separates the “money edge” (expected accounting return) from the “felt edge” (behavioral value) by mapping monetary outcomes through a prospect value function and comparing the two across parameter ranges. The mechanism is parametric and modular, allowing different MEV, cost, and penalty profiles to plug in without altering the base PoS model. Using stylized numerical examples, we identify regions where cooperation that pays in expectation can remain unattractive under plausible loss-averse preferences, especially when penalties are salient or MEV is volatile. We discuss how these distortions may affect validator participation, economic security, and the tuning of rewards and penalties in Ethereum’s PoS. Integrating behavioral valuation into crypto-economic design thus provides a practical diagnostic for adjusting protocol parameters when economics and perception diverge.

1. Introduction

Decentralized financial platforms enabled by blockchain technologies allow individuals to collaborate in a decentralized manner while pursuing the shared objective of gaining profits [1]. Blockchain networks like Bitcoin and Ethereum are built based on incentive mechanisms intended to encourage participants to behave honestly in maintaining the validity of the ledger. In classical designs, these participants are modeled as fully rational economic actants, self-interested individuals who will use the protocol if its use maximizes their expected payoff [2,3]. This rational actor assumption has deep roots in the computer science (CS) literature on Blockchains and distributed consensus, where game theory and mechanism design are employed to align individual incentives systemwide [4]. For example, Bitcoin’s proof-of-work (PoW) consensus offers block rewards and transaction fees so that a miner’s best response in the game-theoretic sense is to honestly extend the longest chain, making the protocol rules a Nash equilibrium under ideal conditions [1,5]. This approach has yielded a rich body of research analyzing miner and validator behavior using tools like Nash equilibrium analysis, Bayesian games, and equilibria of mining competitions [6,7]. Major conferences and journals in security, cryptography, and information systems have featured studies of validator incentives, staking behavior, miner strategies, and protocol compliance in public blockchains, reinforcing the view of humans as economically rational actors [4]. However, humans are not solely driven by narrow economic payoffs [8]. Decades of research in behavioral economics suggest that real decision-makers exhibit bounded rationality, social preferences, and are influenced by cognitive biases and social context [9,10]. The current crypto-economic models may therefore be limited in their ability to predict or explain actual blockchain participant behavior [6]. For instance, miners and token holders may be influenced by risk perception rather than objective expected value [10], may make errors or “noisy” decisions rather than perfect optimizations or may derive utility from sources other than financial reward such as reputational gains, community identity [11], or norms of reciprocity [12]. Indeed, blockchain network participants interact as members of decentralized communities. Even without prior trust, they are able to establish shared records of ownership and agreement, collectively sustaining a system that compels assent and preserves common truths [13]. These motivations fall outside the purview of traditional game-theoretic models that assume a homogenous profit-maximizer [14].

To date, blockchain incentive mechanism design has largely overlooked these social and behavioral dimensions [15]. Most protocols aim to be incentive-compatible for rational actors, but do not account for how real human behavior might systematically deviate from economic rationality or how social dynamics, trust, cooperation, and identity might be harnessed to improve security and participation [6,11]. This gap is increasingly salient as blockchains are deployed in societal contexts where human actions play a significant role in governance decisions in decentralized organizations and user adoption of blockchain systems [16]. In this paper, we argue for incorporating social theory perspectives into blockchain incentive models. By drawing on theories from psychology, economics, and sociology such as prospect theory [10], bounded rationality [14], social exchange theory [14], identity economics [12], hedonic motivation [9], and structuration theory [12], we can enrich the design and analysis of incentive mechanisms beyond the “homo economicus” [17], or human as a fully rational actor, paradigm. The remainder of this paper is organized as follows. First, we review the literature on blockchain incentive mechanisms that model participants as rational economic agents, highlighting key findings and limitations of the game-theoretic approach. We then examine whether and how prior works integrate social or behavioral theories into blockchain models. We conclude the literature review by articulating how incorporating social perspectives addresses the identified research gap and can lead to more robust incentive mechanism design for blockchains.

Emerging trends and real-world applications: our focus on Ethereum’s PoS consensus and MEV reflects blockchain’s role as critical digital infrastructure for payment, DeFi, and data-intensive applications, where system security and energy-efficient operation depend on behaviorally realistic incentive mechanisms.

2. Literature Review

2.1. Proof-of-Work (PoW)|Proof-of-Stake (PoS) and Human Behavior

Bitcoin’s Nakamoto consensus is the seminal example, coupling a PoW puzzle with a block reward incentive [1]. Early economic analyses modeled Bitcoin mining as a game and found that there exists at least one equilibrium where all miners follow the protocol honestly [5]. This result supported the Bitcoin community’s belief that the system could be stable if miners act according to incentives [5]. However, Kroll et al. also points out that infinitely many other equilibria exist in theory where miners behave otherwise, including malicious or collusive strategies [5]. Honest mining is not a dominant strategy but one that leads to equilibrium among many, raising the possibility that without additional coordination or norms, a game-theoretic model cannot guarantee which equilibrium will prevail [18]. Previous research further argues that sustaining the desired equilibrium likely requires governance structures or social coordination mechanisms beyond the bare incentives, foreshadowing the need to consider institutional and social factors in cryptocurrency systems [15]. Soon after, researchers discovered concrete examples of profitable deviant strategies under the rational model [6]. Eyal and Sirer’s seminal work on selfish mining demonstrated that a coalition controlling as little as 25–33% of the total hash power could increase its relative revenue by deviating from honestly following protocol, withholding found blocks, and strategically releasing them [6]. The Bitcoin protocol as implemented did not induce a unique Nash equilibrium at honest behavior; a rational minority could gain more than its fair share, contradicting the assumption that >50% would be needed to compromise the system [19]. The selfish mining result showed that above a certain threshold of hashing power, a miner coalition’s payoff rises linearly with its size, incentivizing rational miners to join the selfish pool [6]. This positive feedback could lead to centralization or majority attacks if miners purely follow short-term economic incentives [20]. Indeed, Eyal and Sirer concluded that in the unmodified Bitcoin protocol, honest mining does not lead to a Nash equilibrium under realistic network conditions [6]. Their analysis prompted protocol adjustments such as publishing penalties and changes to block reward rules to raise the threshold at which selfish mining is viable aiming to enforce honesty at least up to 25% of hash power [21,22].

Following these findings, a large body of work examined miner behavior and protocol compliance through a game-theoretic lens. Validator strategies in proof-of-work have been studied in terms of mining difficulty adjustments, mining pool formation, block propagation games, and transaction fee auctions [23]. For example, researchers have explored the miners’ dilemma in transaction fee selection and the stability of mining pools as coalitions often using cooperative game theory or equilibrium analysis [24,25]. Notably, the finance and economics community has also contributed, with studies in journals like Review of Financial Studies and Journal of Finance analyzing Bitcoin through economic equilibrium models [18]. For instance, Biais et al. proved a “blockchain folk theorem” showing that many equilibria—some good, some bad—can exist in repeated blockchain games depending on miners’ beliefs and coordination [18]. Budish examined the cost of attacking Bitcoin and argued there are fundamental economic limits to its security, highlighting the trade-off between transaction throughput and incentive compatibility [26]. These works reinforce that Nash equilibrium and game-theoretic reasoning are core to understanding blockchain security in the rational actor paradigm [5,6,18].

As blockchain designs evolved, researchers turned their attention to proof-of-stake systems (e.g., Ethereum 2.0’s Casper [27], Cardano’s Ouroboros [4], Algorand [28]) where validators stake cryptocurrency instead of expending energy. Initially, many PoS protocols were analyzed in the traditional Byzantine fault tolerance model, assuming a threshold of honest players (e.g., ≥2/3 honest) without explicitly modeling economic incentives [29,30]. However, recognizing the importance of incentives, recent works have applied game theory to validator behavior and staking decisions [3,31].

Beyond Chen and Golab’s Eth2 incentive analysis [3], a growing body of Ethereum-focused engineering work highlights how protocol-level design choices affect real-world applications. Tseng et al. use Ethereum-based smart contracts to build a trustworthy rental market architecture, showing how incentive-compatible recordkeeping and automated enforcement can support housing applications in practice [32]. Khan et al. propose a decentralized payment framework tailored to low-connectivity environments using Ethereum blockchains, illustrating how network constraints and security requirements shape protocol and incentive choices [33]. These studies underline that Ethereum’s PoS incentives are embedded in broader socio-technical systems, but they still treat validators as rational actors and do not explicitly model behavioral valuation.

One thread of research asks: Does following the PoS protocol lead to a Nash equilibrium for rational token holders, or do attacks like “nothing-at-stake” or bribery yield higher payoffs? [34] Studies have modeled validators’ choices of which fork(s) to mine on, whether to equivocate or double-sign when there is a chance to gain from multiple chains), and how much stake to lock up, using equilibrium analysis [35]. For example, Kiayias et al. prove that under certain assumptions such as honest majority of stake and network synchrony, protocols like Ouroboros are secure, but these proofs often assume participants either follow the protocol or act arbitrarily (Byzantine) [4,35]. Subsequent analyses allowed for rational adversaries, and others studied “stake grinding” and liveness issues when validators rationally delay or manipulate randomness, while Badertscher et al. modeled rational players in PoS and identified conditions for incentive compatibility [35]. A key result across these works is that designing incentives in PoS is delicate—e.g., one must introduce slashing conditions so that creating conflicting blocks or deviating is economically irrational [36]. Recent game-theoretic frameworks explicitly incorporate multi-layer incentives in blockchain systems [37]. A 2025 study by Avarikioti et al. [37] proposes a composable game-theoretic framework covering the consensus layer, network layer, and application layer simultaneously, noting that traditional analyses often focused on one layer at a time and missed cross-layer incentive effects. They observe that earlier models were either purely cryptographic (honest vs. Byzantine with no economic calculus) or “monolithic” rational models that abstracted away network and application interactions [37]. By contrast, their framework aims to reason for complex scenarios like miners bribed via smart contracts (e.g., time-locked bribery attacks) and MEV (maximal extractable value) exploits that span multiple protocol layers [37,38]. The rational-agent incentive models have yielded fundamental insights and are now a cornerstone of blockchain systems design [39].

By requiring that honest protocol compliance be a Nash equilibrium or a dominant strategy, in an ideal case, protocol designers strive to make the system robust against selfish deviations [6,31]. This paradigm has driven innovations like mechanism design for transaction fee markets such as EIP-1559 in Ethereum, which is designed to be game-theoretically optimal for users and miners, and analyses of protocol changes through the lens of equilibria [40]. Nevertheless, this literature also highlights its own limitations: when making simplifying assumptions to ensure analytical tractability, models often treat participants as identical, perfectly rational, and motivated only by direct monetary payoffs.

In reality, miners and validators are human-operated or human-influenced entities that may not behave like anonymous rational profit-maximizers in one-shot games. Additionally, rational models can predict undesirable equilibria such as formation of a cartel, or certain attacks that, in practice, have not always materialized, possibly because real participants consider the long-term welfare of the network, possess ethical commitments, or face social repercussions for misbehavior [41]. These observations raise the question: Could incorporating richer models of human behavior improve our understanding of blockchain incentives? We turn next to the literature that begins to bridge this gap by introducing behavioral and social theoretical perspectives.

2.2. Integrating Behavioral and Social Perspectives

While still an emerging area, some researchers have started to relax the strict homo economicus assumption in blockchain models, drawing on behavioral economics and social science theories to better capture how real participants might behave [15,36]. We review several such efforts, including applications of prospect theory, bounded rationality models (quantal response equilibrium), evolutionary game theory, and early explorations of social/organizational factors. We also highlight the paucity of studies incorporating concepts like identity, social norms, and intrinsic motivation into blockchain incentive design, underscoring an opportunity for further research.

Prospect theory, developed by Kahneman and Tversky, posits that individuals evaluate gains and losses relative to a reference point and exhibit loss aversion and probability distortion [10]. This theory recognizes that humans often violate the expected utility paradigm assumed in classical game theory [10]. A few blockchain-related works have leveraged prospect theory to model participant decisions under risk and uncertainty [42]. By introducing the difference between perceived value and actual payoff, they account for decision-makers’ rationality deficits and subjective preferences, bringing the model’s predictions closer to observed behavior [42]. Their results show that when agents’ loss aversion and risk attitudes as characterized by prospect theory parameters are considered, the system’s evolutionary stable strategy shifts, implying different levels of participation or compliance than a traditional expected-value model would predict [42]. Finite rational agents under prospect theory may, for instance, shy away from a strategy with a higher expected value if it involves the possibility of a salient loss, a scenario quite relevant to blockchain contexts like staking, where agents risk losing deposits (slashing) and may behave more conservatively than risk-neutral models predict. By incorporating prospect-theoretic utility, these models capture such psychological factors explicitly. However, it must be noted that these applications have so far been in specific settings such as government incentives for blockchain-based data sharing rather than mainstream consensus protocol design [42]. Nonetheless, they illustrate the methodological feasibility and value of accounting for human biases in incentive models: the outcomes of the game can change qualitatively when agents are assumed to be loss-averse rather than perfectly rational [9]. This opens the door to applying prospect theory to problems like miner investment decisions where miners might outweigh the chance of hitting a block reward jackpot or stake-holder participation in governance where fear of losses might make them stick with status quo policies.

Another line of work addresses the fact that participants may not find or play exact best responses as Nash equilibrium assumes, especially in complex, dynamic environments like blockchain networks [8]. Instead of assuming flawless optimization, models of bounded rationality allow for noisy or approximate decision-making [43].

One popular framework is the quantal response equilibrium (QRE), in which agents are more likely to choose better strategies but are not guaranteed to choose the absolute best they have a stochastic choice function often modeled by a logit distribution [43,44]. This approach has been used to model miner strategies in blockchains. For instance, Nadendla and Varshney examine a mining auction game modeling how miners invest effort/hash power and assume that miners’ strategies converge to a QRE rather than a pure Nash equilibrium [45]. In their model, a miner sometimes “over-exerts” or “under-exerts” effort relative to the Nash prediction, due to random utility shocks [45]. Interestingly, their analysis found that quantal response strategies can lead to greater participation than the Nash equilibrium would suggest [45]. Intuitively, if miners are not perfectly optimizing, some will occasionally invest more in mining even when it is marginally suboptimal, which increases overall network effort and could enhance security or, conversely, make the difficulty adjustment unstable [25]. They formalize this by introducing a continuous logit model for miners’ utility, where each miner’s probability of choosing a certain effort level increases with the payoff of that effort [45]. As the “rationality parameter” in the logit function varies, one can interpolate between fully random behavior and perfectly best-responding behavior [43,45]. QRE provides a more realistic equilibrium concept for scenarios where players have limited information or computational ability to find the best response.

By applying QRE, blockchain researchers can capture decision errors, experimentation, and heterogeneity in participant behavior. Similarly, evolutionary game theory and learning models have been used to understand how consensus might be achieved not as a static equilibrium from inception, but as an outcome of agents adapting over time [46]. Zhang and Tian, for example, model blockchain consensus as a repeated game in which agents imitate successful strategies and learn from global history, using an evolutionary dynamics approach [47]. They introduce a bounded rationality solution concept and identify different stable equilibria—including an “honest” equilibrium where agents cooperate by following the protocol—under various initial conditions [47]. By evaluating outcomes in terms of social welfare in addition to standard security metrics, their study crosses into what they call cooperative AI, blending computing and social science insights [47]. The key contribution of such works is acknowledging that agents in blockchain systems might learn and adjust their behavior over time, rather than being omniscient rational actors from the start. This dynamic view can illuminate why, for instance, blockchain communities often go through periods of instability—forks, attacks—that eventually stabilize as participants converge on norms or as deviators are ostracized, an outcome that a one-shot Nash analysis might miss [15,26].

Perhaps the most nascent and challenging frontier is incorporating social theory, the idea that participants are influenced by social context, roles, and non-economic motives [48]. In the broader IS literature, it is well established that technology adoption and use are driven by factors like social influence, trust, enjoyment, and institutional structures [49]. A number of studies have applied these theories to blockchain at a macro level [50,51]. Others have extended technology acceptance models (TAM/UTAUT) to blockchain applications, finding that hedonic motivation—the fun or satisfaction from using a novel technology—and social norms can significantly influence a user’s intention to use cryptocurrency or decentralized platforms [52]. These works, however, typically focus on end-user or organizational adoption of blockchain systems such as deciding to implement a blockchain for supply chain management rather than the internal mechanics of consensus protocols [51]. Additionally, we found very few studies in the blockchain protocol literature that formalize social or identity-driven utility. One notable exception is an analysis by Kovalchuk et al. of blockchain governance, which contrasts “Rational Delegates” vs. “Emotional Delegates” in a voting game for funding proposals [53]. In their model, emotional delegates are those who may vote against their narrow financial interest, for example, due to personal attachment to a project or moral stance against bribery [53]. They derive utility not just from monetary rewards but also from intangible factors [53]. The authors derive conditions under which no bribery occurs in equilibrium, essentially requiring that both proposers and delegates have sufficiently high aversion to the act of bribery [53]. Although this study is in the context of decentralized governance rather than block creation, it is a step toward recognizing that identity and ethical preferences can be crucial: a delegate who identifies as a faithful steward of the blockchain’s mission might reject a lucrative bribe, a behavior inexplicable by pure profit calculus but explainable by identity utility or social reputation concerns [53,54]. More broadly, the concept of identity in utility in Akerlof and Kranton’s framework explains where people gain utility from conforming to norms of a social category with a clear relevance to blockchain communities [54].

Additionally, on another aspect of behavior, miner altruism has occasionally been observed, for instance, miners sticking with a coin because they believe in its vision, even when mining it is less profitable than alternatives [55]. The classical model would deem such behavior “irrational”, but an identity economics lens sees it as rational once the miner’s utility is expanded to include pride in supporting the network or aligning with a “decentralist” identity [11,54]. To our knowledge, no formal blockchain incentive model yet includes an identity term in the utility function; this remains an open research opportunity. Nonetheless, previous quantitative and qualitative studies suggest that these factors are at play. For example, trust and reciprocity have been discussed in blockchain governance, the notion of a ”social contract” among miners and developers [56]. This argument implies that ultimately, the security of open blockchains may rest on social constraints, attackers choosing not to attack due to normative reasons, or community enforcement since any purely incentive-based assumption can be broken by a clever enough adversary [56]. Rationality alone is “self-defeating” in permissionless systems unless buttressed by either stronger assumptions like identity verification or acceptance that some participants behave altruistically or adhere to ethical norms [11,54]. This perspective encourages system designers to consider Byzantine–Altruistic–Rational (BAR) models—a mix of player types—or to integrate social science insights on how to foster cooperation [57]. From an IS theoretical standpoint, frameworks like structuration theory and actor-network theory have been invoked to describe blockchain as not just a technology, but as a socio-technical system where human agency and technological structures mutually shape each other [58]. These frameworks claim that blockchain networks consist of social sub-systems, developers, miners, exchanges, and users embedded in institutions and subject to governance, not merely anonymous economic actors interacting with code. While such high-level analyses exist, they have not yet penetrated the core of incentive mechanism design.

Overall, prior work on blockchain incentives falls into three broad streams. A first stream in computer science and cryptography develops formal, rational-actor models of consensus and incentive compatibility in PoW and PoS systems, including Bitcoin mining games, mining pool strategies, and formal analyses of Eth2 rewards and penalties [2,3,4,5,6,7]. A second stream overlays social and behavioral perspectives on blockchain governance and participation, drawing on identity economics, social norms, and socio-technical systems theory to argue that miners and validators are guided by more than narrow expected payoffs [11,54,56,57,58]. A third, more applied stream designs Ethereum-based architectures for domains such as rental markets, payments, and supply chains, where protocol parameters and gas economics directly constrain real-world applications [32,33,50,51,52]. What is currently missing is a formal incentive model that combines the slot-level specificity of the first stream with the behavioral realism of the second stream, applied to an Ethereum PoS setting that matters for the third stream. This is precisely the niche that our prospect-theoretic PT-IM mechanism aims to fill.

3. PT-IM (Prospect-Theoretic Incentive Mechanism)

3.1. Benchmark Model’s Mechanism

To ground our mechanism adjustments, we adopt Chen and Golab’s formal study of Ethereum 2.0 (Eth2) as our benchmark model [3]. Their paper builds a slot-level, game-theoretic analysis of validators introducing block proposers and attesters under the canonical proof-of-stake (PoS) reward/penalty rules and proves incentive-compatibility in that setting [3]. We summarize their model and findings here and position it as the reference point from which our “Social Actant” adjustments depart based on prospect theory.

In Ethereum 2.0, validators perform three primary duties, proposing blocks that extend the chain head, attesting to the source/target/head checkpoints within each epoch, and periodically serving on a 512-member sync committee that signs block headers [3]. Rewards and penalties accrue to validators conditional on how faithfully these duties are performed; slashing also applies to specific rule violations; whereas this operational incentive mechanism is the basis for the paper’s formal reward and penalty accounting [3].

Chen and Golab first “disassemble” Eth2 incentives into three components: rewards, penalties, and costs, whereas rewards comprise (i) attestation rewards, (ii) proposer rewards, and (iii) sync-committee rewards [3].

Penalties mirror the reward structure where attesters incur penalties equal to the foregone reward when they vote incorrectly for a source or target, but notably there is no penalty for an incorrect head vote, an asymmetry the authors highlight later in their analysis [3]. Motivated by heterogeneity and incomplete information in real-world PoS settings, the authors cast validator interaction within a Bayesian game rather than a complete-information strategic game [3].

3.2. PT-IM (Prospect-Theoretic Incentive Mechanism)

Our proposed PT-IM (Prospect-Theoretic Incentive Mechanism) proceeds in three setup steps to ground later details: (1) Benchmark specification: adopt the Chen–Golab game-theoretic mechanism for Ethereum PoS as the rational, money-based baseline. (2) Prospect overlay: apply a prospect-theory mapping to the same reward/penalty and cost components, fixing a reference point and allowing asymmetric valuation of gains vs. losses (loss aversion) with simple probability reweighing to convert baseline cash outcomes into behaviorally adjusted valuations. (3) Comparative assessment: compute the difference between the PT-valued incentive result and the baseline result, interpreting the gap as the incremental effect of risk aversion and unequal perception of gains and losses. This scaffold establishes the foundation for the subsequent, stepwise formalization and parameter choices. The following subsections present each step in detail.

3.2.1. Step 1—Benchmark Specification

A key limitation of the Chen–Golab benchmark is that it does not explicitly model proposer MEV (maximal extractable value) which is the additional revenue a proposer can realize by reordering, including, or excluding transactions. Step 1 addresses this by introducing MEV as an explicit parameter that activates only when the actant is the slot proposer, thereby augmenting the baseline consensus payout with a proposer-conditional component that is naturally prospect-theoretic where MEV is volatile, skewed, and tail-heavy, so its perceived value can differ markedly from its expected value under loss aversion and probability weighting. Operationally, the step preserves the Chen–Golab accounting in which an actant’s baseline money is the consensus reward, from which penalties and real operating costs (e.g., electricity, bandwidth, hardware/ops) are deducted. Because the model is game-theoretic, each round the actant chooses between cooperation and deviation, yielding two distinct payoff expressions whereas one that includes consensus reward minus penalties and costs, and one that forgoes reward and costs but may still incur penalties setting the stage for comparing the two actions under both rational and prospect-adjusted valuations.

Continuing from the extension, the mechanism treats each slot as occurring in one of several possible “states” (e.g., proposer vs. attester) and assigns to each state a pair of action-conditional probabilities, the probability that the actant cooperates in that state and the complementary probability that it deviates. These per-state actions sum up to one, so every state fully allocates behavior between the two choices. The expected monetary outcome for cooperation is then obtained by averaging that action’s per-state payoffs. The expected outcome for deviation is computed similarly by averaging the deviation payoffs. Comparing these two expectations yields the economic edge of cooperation/deviation for the slot.

Definition 1.

Step 1—Benchmark Specification

(a)

Baseline reward

$$R=R_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}}+\mathbf{1}\left\{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{o}\mathrm{s}\mathrm{e}\mathrm{r}\right\}·\mathrm{M}\mathrm{E}\mathrm{V}.$$

(b)

State outcomes under Cooperate vs. Deviate

$$x_C\left(j\right)=R_j-P_j-C, x_D\left(k\right)=-P_k.$$

(c)

Probabilities of state

$$\mathrm{S}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{e}: \mathcal{S}=\{P_1,P_2,P_3,\dots \}.$$

$$\mathrm{Per}–\mathrm{staeactionmix} \forall s\in \mathcal{S}: p_s^C\ge 0, p_s^D\ge 0, \boxed{p_s^C+p_s^D=1}.$$

(d)

Expected Value of money under each choice

$$E\left[x_C\right]=E\left[R\right]-E\left[P\right]-C, E\left[x_D\right]=-E\left[P\right],$$

where $E\left[R\right]={\sum }_j{p}_j{R}_j, E\left[P\right]={\sum }_j{p}_j{P}_j (\mathrm{o}\mathrm{r} {\sum }_k{q}_k{P}_k \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n} \mathrm{e}\mathrm{v}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} D).$

(e)

Economic edge of Cooperation over Deviation

$${\Delta }_{\$}\equiv E\left[x_C\right]-E\left[x_D\right]=E\left[R\right]-C.$$

3.2.2. Step 2—Prospect Overlay

The prospect-theoretical perception layer converts the Step 1 outcomes into perceived utilities by anchoring the evaluation to a reference that represents typical cooperative earnings including proposer side revenue when applicable. Each realization is split into gains and shortfalls relative to this anchor which captures the empirical asymmetry that losses hurt more than equal sized gains please. Cooperative outcomes are re-expressed along four dimensions where upside rewards feel muted due to diminishing sensitivity where shortfalls below the reference are emphasized through loss aversion, where protocol penalties carry extra sting beyond their nominal size, and where ongoing operating costs receive their own disutility weight. Deviation records no reward and no operating cost yet still applies to any penalties which lie on the loss side and thus feel especially painful. Expected perceived utilities for cooperation and deviation are obtained by averaging these per state perceptions with the same state probabilities used in the baseline, and their difference supplies the prospect-theoretical decision signal that indicates whether cooperation feels at least as attractive as deviation.

As mentioned before about the theory, the prospect-theoretical formulas are drawn from Kahneman and Tversky’s Prospect Theory 1979 and its cumulative form, Tversky and Kahneman 1992 [10], and are tailored to this mechanism while preserving the original behavioral economics primitives of reference dependence loss aversion diminishing sensitivity and probability weighting as specified by authors. Accordingly, this layer of the mechanism introduces a small set of interpretable knobs which include a reward dampener that governs how quickly excitement from upside saturates a gain side curvature that encodes diminishing sensitivity a shortfall or loss aversion weight that determines how strongly falling below the reference hurts a penalty weight that amplifies the sting of rule based penalties a cost weight that captures the burden of ongoing operating expenses and optional probability weighting for rare events.

Definition 2.

Step 2—Prospect Overlay

(a)

Reference (comfort line)

$$r=\mathbb{E}\left[R\right]-C.$$

(b)

Positive-part operator and gain/shortfall split

$$[z{]}_{+}=\mathrm{m}\mathrm{a}\mathrm{x}\{z,0\}, \mathrm{g}\mathrm{a}\mathrm{i}\mathrm{n}:[R_j-r{]}_{+}, \mathrm{s}\mathrm{h}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{f}\mathrm{a}\mathrm{l}\mathrm{l}:[r-R_j{]}_{+}.$$

(c)

Per-state felt value under Cooperate

$$V_C\left(j\right)=\kappa [R_j-r{]}_{+}^{{\alpha }_g}-{\lambda }_0[r-R_j{]}_{+}^{{\alpha }_{\mathcal{l}}}-{\lambda }_p{P}_j^{{\alpha }_{\mathcal{l}}}-{\lambda }_c{C}^{{\alpha }_{\mathcal{l}}}.$$

(d)

Per-state felt value under Deviate

$$V_D\left(k\right)=-{\lambda }_0[r-0{]}_{+}^{{\alpha }_{\mathcal{l}}}-{\lambda }_p{P}_k^{{\alpha }_{\mathcal{l}}}.$$

(e)

Expected perceived utilities and PT edge

$$U_C={\sum }_j{p}_j{V}_C(j), U_D={\sum }_k{q}_k{V}_D(k), \boxed{{\epsilon }^{\mathrm{P}\mathrm{T}}=U_C-U_D}$$

(f)

Multiplier and curvature multipliers

$$\kappa \in \left(\mathrm{0,1}\right], {\alpha }_g\in \left(\mathrm{0,1}\right], {\alpha }_{\mathcal{l}}\in \left(\mathrm{0,1}\right], {\lambda }_0>1, {\lambda }_p>1, {\lambda }_c>1.$$

These parameters can be estimated from revealed preference logs using observed actions under known outcomes from choice experiments that elicit accept or decline decisions under synthetic reward and penalty profiles or from historical records matched to network conditions. The prospect layer does not alter Step 1 accounting but it re-values the same monetary ingredients and state probabilities and thereby provides a behaviorally grounded lens for incentive comparison.

3.2.3. Step 3—Comparative Assessment

This step places the two results produced earlier side by side using the same state space and probabilities from Step 1. The first result is the economic or money edge from Step 1 which asks whether cooperation pays more in expectation after consensus rewards proposer-conditional MEV penalties and operating costs are accounted for. The second result is the prospect-theoretic or felt edge from Step 2 which asks whether cooperation feels at least as attractive as deviation once outcomes are revalued through reference dependence loss aversion diminishing sensitivity and the designated weights on penalties and costs. No additional smoothing transformations or probability changes are introduced here so Step 3 is a pure comparison that keeps the accounting and the state weights fixed.

Interpretation follows a simple sign-based rule. If both the money edge and the felt edge are positive the mechanism both pays and feels pro cooperation. If the money edge is positive but the felt edge is negative the system pays to cooperate yet feels worse to the actor indicating a behavioral gap that may be addressed by parameter tuning or mechanism adjustments. If the felt edge is positive while the money edge is negative the actor is drawn to cooperate despite unfavorable economics which flags model inputs or operational assumptions for review. If both are negative cooperation is unattractive on both grounds. Reporting both results together makes it transparent whether incentive alignment holds economically behaviorally or both.

Definition 3.

Step 3—Comparative Assessment

(a)

Expected money from Step 1

$$E\left[x_C\right]=E\left[R\right]-E\left[P\right]-C, E\left[x_D\right]=-E\left[P\right],$$

$$\boxed{{\Delta }_{\$}=E\left[x_C\right]-E\left[x_D\right]=E\left[R\right]-C}, E[R]={\sum }_j{p}_j{R}_j, E[P]={\sum }_j{p}_j{P}_j$$

(b)

Expected perceived Utility from Step 2

$$U_C={\sum }_j{p}_j{V}_C(j), U_D={\sum }_k{q}_k{V}_D(k), \boxed{{\epsilon }^{\mathrm{P}\mathrm{T}}=U_C-U_D}.$$

(c)

Decision table

$$\begin{array}{lll}{\mathbf{\Delta }}_{\mathbf{\$}}& {\mathit{\epsilon }}^{\mathbf{P}\mathbf{T}}& \mathbf{I}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{p}\mathbf{r}\mathbf{e}\mathbf{t}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\\ \ge 0& \ge 0& \mathrm{G}\mathrm{o}\mathrm{o}\mathrm{d}:\mathrm{C}\mathrm{p}\mathrm{a}\mathrm{y}\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{f}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{a}\mathrm{t}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{g}\mathrm{o}\mathrm{o}\mathrm{d}.\\ \ge 0& <0& \mathrm{M}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{y}\mathrm{s}\mathrm{a}\mathrm{y}\mathrm{s}\mathrm{C},\mathrm{f}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}\mathrm{s}\mathrm{a}\mathrm{y}\mathrm{D}\left(\mathrm{b}\mathrm{e}\mathrm{h}\mathrm{a}\mathrm{v}\mathrm{i}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{g}\mathrm{a}\mathrm{p}\right).\\ <0& \ge 0& \mathrm{F}\mathrm{e}\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{l}\mathrm{i}\mathrm{k}\mathrm{e}\mathrm{C},\mathrm{b}\mathrm{u}\mathrm{t}\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{e}\mathrm{y}\mathrm{s}\mathrm{a}\mathrm{y}\mathrm{s}\mathrm{D}(\mathrm{c}\mathrm{h}\mathrm{e}\mathrm{c}\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{p}\mathrm{u}\mathrm{t}\mathrm{s}/\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}).\\ <0& <0& \mathrm{B}\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{s}\mathrm{a}\mathrm{y}\mathrm{D};\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}.\end{array}$$

The construction is parametric and estimable, so parameters can be calibrated on logs or experiments and stress-tested with sensitivity analyses, while MEV variability, penalty schedules, and operating cost profiles can be swapped in without altering the foundations. The extended mechanism is intended for design iteration and policy tuning, enabling targeted adjustments when economics and perception diverge, and it remains extensible to richer behaviors or alternative payoff components as needed.

3.2.4. Calibration Considerations and a Numeric Example

In this paper we treat the prospect-theoretic parameters (α, β, λ, γ) as exogenous and explore their qualitative impact on Ethereum PoS incentives. In practice, these parameters could be estimated from several data sources. One path is to infer them from validator-behavior logs and historical block proposal/attestation patterns by fitting PT-IM to observed deviations from rational best responses (e.g., missed attestations around large MEV events). A second path is to run incentivized lab or field experiments with validators or experienced Ethereum users, eliciting their risk and loss preferences in PoS-like gambles. A third path is to use survey-based or staking-platform data to estimate how different penalty and reward regimes affect validator entry and exit decisions.

To make the gap between the “money edge” and the “felt edge” concrete, consider a simple slot in which a cooperative validator expects a baseline reward of +0.8 units, incurs operating costs of −0.3 units, and faces a small 5% chance of a −2.0 unit penalty. The expected monetary value of cooperation is therefore +0.40 units, and if deviating yields −0.10 units, the rational money edge of cooperation is +0.50. Under prospect theory, however, both the size and likelihood of losses are distorted: with standard parameters (α = β = 0.88, λ = 2.25, γ = 0.61), the −2.0 penalty is psychologically amplified to roughly −4.1 units due to loss aversion, and its 5% probability is overweighted to about 17%. This produces a perceived penalty impact of about −0.70, far larger than the monetary −0.10. When combined with value curvature on gains and costs, the behavioral valuation of cooperative outcomes becomes approximately −0.52. In other words, cooperation feels negative even though it is objectively profitable, illustrating how modest penalty risks and loss aversion can create a negative “felt edge” despite a positive money edge, making cooperative behavior seem unattractive to real validators.

4. Concluding Remarks

Behaviorally distorted incentives have several concrete implications for Ethereum protocol engineering. First, if validators outweigh salient slashing or penalty events, cooperation may require higher baseline rewards or softer penalties than predicted by rational models, affecting economic security margins. Second, where MEV is highly volatile and skewed, prospect distortions can make proposer roles feel like lottery tickets, which may in turn motivate MEV smoothing, redistribution, or protocol-level auctions to stabilize the perceived reward profile. Third, loss aversion around downtime and correlated failures suggests that reward and penalty tuning should consider not only expected values but also how compressed or dispersed the perceived outcome distribution is. Finally, because Ethereum’s PoS replaces the energy-intensive security of PoW with staked capital and validator behavior, prospect-theoretic misalignment between money and felt edges becomes a systems-engineering concern: the reliability, energy efficiency, and decentralization of the network hinge on incentives that feel robust to real human validators.

This paper introduced a Prospect-Theoretic Incentive Mechanism (PT-IM) for Ethereum’s proof-of-stake, overlaying a canonical Eth2 reward and penalty model with a behavioral valuation that separates the money edge from the felt edge of cooperation. By embedding prospect theory into a slot-level incentive analysis with proposer MEV, costs, and penalties, we showed how loss aversion and probability weighting can render economically sound cooperative strategies behaviorally unattractive under plausible parameter configurations. The results highlight specific regions of the parameter space—highly salient penalties, volatile MEV, thin margins—where protocol incentives may need to be adjusted if designers want cooperation to feel as attractive as it looks on paper.

4.1. Limitations

The mechanism has not yet been implemented in a real setting; therefore, the prospect-theoretic multipliers and curvatures have not been estimated from validator specific behavior. The work does not identify or resolve the challenges that arise when actors behave maliciously or when the consensus layer is compromised, including coordinated attacks, censorship, and widespread network failures. Additionally, the model abstracts from intertemporal effects, cross slot learning, liquidity constraints, and portfolio level risk management by operators. It assumes a stable environment for rewards, penalties, costs, and MEV distributions, which may drift with market structure and policy changes. These limits reflect the intent of the work as a mathematical scaffold built on prior models, intended to serve as a starting point for empirical validation, field calibration, and robust studies in future research.

4.2. Future Work

Future work will address the identified limitations by calibrating the prospect-theoretic multipliers and curvatures with validator level data validating the mechanism in tested or shadow deployments and stress testing behavior under adversarial and degraded consensus conditions. Additional priorities include explicit treatment of slashing pathways and correlated failures improved identifiability and uncertainty quantification for behavioral parameters and systematic sensitivity analyses to distribution shifts in rewards penalties costs and MEV. Hence, the present research operationalizes only prospect theory, yet human decision-making is shaped by a broader set of social and behavioral frameworks, such as cumulative prospect variants, rank dependent utility, reference dependent risk, preferences, ambiguity, attitudes, social norms, and reciprocity, all of which can be quantified and embedded in blockchain incentive design. Advancing along these directions will transform the current mathematical scaffold into a validated policy tool that links behavioral realism with robust protocol engineering.