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on Game Theory |
| By: | Francesc Dilmé |
| Abstract: | A Nash equilibrium of a game in extensive form is a sequential equilibrium in mixed strategies if it can be approximated through equilibria of close-by games with slightly perturbed payoffs and small-probability behavioral types. We show that sequential equilibria in mixed strategies are equivalent to (i) weakly sequential equilibria (Reny, 1992), (ii) normal-form perfect equilibria (Selten, 1975) in games with generic payoffs, and (iii) purifiable Nash equilibria (Harsanyi, 1973). A corollary of our results is that extensive-form perfect equilibria are normal-form perfect equilibria in games with generic payoffs. |
| Keywords: | Sequential equilibria, mixed strategies, purification |
| JEL: | C72 C73 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_703 |
| By: | Philippe de Donder (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Humberto Llavador (UPF - Universitat Pompeu Fabra [Barcelona]); Stefan Penczynski (UEA - University of East Anglia [Norwich]); John E. Roemer (Yale University [New Haven]); Roberto Vélez-Grajales (Auteur indépendant) |
| Abstract: | The vaccination game exhibits positive externalities. The standard game-theoretic approach assumes that parents make decisions according to the Nash protocol, which is ndividualistic and non-cooperative. However, in more solidaristic societies, parents may behave cooperatively, optimizing according to the Kantian protocol, in which the equilibrium is efficient. We develop a random utility model of vaccination behavior and prove that the equilibrium coverage rate is larger with the Kant protocol than with the Nash one. Using survey data collected from six countries, we calibrate the parameters of the vaccination game, compute both Nash equilibrium and Kantian equilibrium profiles, and compare them with observed vaccination behavior. We find evidence that parents demonstrate cooperative behavior in all six countries. The study highlights the importance of cooperation in shaping vaccination behavior and underscores the need to consider these factors in public health interventions. |
| Keywords: | free-rider problem, measles vaccination, Nash equilibrium, Kantian equilibrium |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05285397 |
| By: | Francesc Dilmé |
| Abstract: | An equilibrium outcome of a game in extensive form is fully self-justifiable if it is supported by justifiable equilibria (McLennan, 1985) regardless of the order in which actions implausible under the given outcome are excluded. We show that the set of fully self-justifiable outcomes is non-empty and contains the set of sequentially stable outcomes (Dilmé, 2024). In signaling games, fully self-justifiable outcomes pass all the selection criteria in Cho and Kreps (1987). Full self-justifiability allows for the systematic use of the logic of selection criteria in signaling games to select equilibria in any finite extensive form game. |
| Keywords: | Justfiable equilibira, sequentially stable outcomes |
| JEL: | C72 C73 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_702 |
| By: | Martínez Martínez, Ismael; Normann, Hans-Theo |
| Abstract: | We analyze infinitely repeated multiplayer prisoner's dilemmas in continuous-time experiments. As the number of players changes, our design keeps the payoffs of the all-defection, all-cooperation, and unilateral- defection and -cooperation outcomes constant, thus controlling for the minimum discount factor required for cooperation to be an equilibrium. For all group sizes, we study three different variants of the prisoner's dilemma. In further treatments, we allow actions to be chosen from a continuous set. We find that cooperation rates decrease with the number of players, a result that we can attribute to the increased strategic uncertainty in larger groups. The different payoff matrices also affect cooperation. For the payoff matrices with lower levels of cooperation, the group-size effect is weaker. The availability of a continuous action set strongly reduces cooperation rates. |
| Keywords: | cooperation, dilemma, experiment |
| JEL: | C72 C73 C92 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:dicedp:327128 |
| By: | Kevin He (University of Pennsylvania); Jonathan Libgober (University of Southern California) |
| Abstract: | We extend the indirect evolutionary approach to the selection of (possibly misspecified) models. Agents with different models match in pairs to play a stage game, where models define feasible beliefs about game parameters and about others’ strategies. In equilibrium, each agent adopts the feasible belief that best fits their data and plays optimally given their beliefs. We define the stability of the resident model by comparing its equilibrium payoff with that of the entrant model, and provide conditions under which the correctly specified resident model can only be destabilized by misspecified entrant models that contain multiple feasible beliefs (that is, entrant models that permit inference). We also show that entrants may do well in their matches against the residents only when the entrant population is large, due to the endogeneity of misspecified beliefs. Applications include the selection of demand-elasticity misperception in Cournot duopoly and the emergence of analogy-based reasoning in centipede games. |
| Keywords: | misspecified Bayesian learning, endogenous misspecifications, evolutionary stability, analogy classes |
| Date: | 2025–09–19 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:25-020 |
| By: | Ehrhart, Karl-Martin; Eicke, Anselm; Hirth, Lion; Ocker, Fabian; Ott, Marion; Schlecht, Ingmar; Wang, Runxi |
| Abstract: | This paper proposes a game-theoretic model to analyze the strategic behavior of inc-dec gaming in market-based congestion management (redispatch). We extend existing models by considering incomplete information about competitors' costs and a finite set of providers. We find that inc-dec gaming is also a rational behavior in markets with high competition and with uncertainty about network constraints. Such behavior already occurs in our setup of two regions. Comparing market-based redispatch with three theoretical benchmarks highlights a lower efficiency level of market-based redispatch and inflated redispatch payments. Finally, we study seven variations of our basic model to assess whether different market fundamentals or market design changes mitigate incdec gaming. None of these variations eliminate inc-dec gaming entirely. |
| Keywords: | Energy market, Game theory, Auctions/bidding, Congestion management, Inc-dec gaming |
| JEL: | D43 D44 L13 Q41 Q48 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:zewdip:327112 |
| By: | Linnenbrink, Daniel |
| JEL: | C72 D44 D47 D82 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:vfsc25:325443 |
| By: | Bos, Olivier; Fugger, Nicolas; Onderstal, Sander |
| Abstract: | We investigate profit-share auctions in a procurement context, comparing them with traditional cash auctions to identify which mechanism yields lower expenses for buyers. We also explore whether specifying a high project value in profit-share auction contracts influences supplier bidding behavior. Using theoretical analysis and experimental methods, we observe that profit-share auctions lead to lower buyer expenses compared to traditional cash auctions. Furthermore, we find that the buyer benefits from specifying a high project value in the contract, as this commitment induces more aggressive bidding from the suppliers. While profit-share auctions result in significantly lower buyer expenses than cash auctions, the observed differences are smaller than predicted. This discrepancy is due to (i) more pronounced underbidding in cash auctions and (ii) lower efficiency in profit-share auctions caused by noisy bidding. Our findings suggest that managers can reduce procurement costs by adopting profit-share auctions and strategically committing to a high project value in contracts. However, they should be aware that real-world savings may be smaller than theoretically predicted due to supplier bidding behavior. |
| Keywords: | procurement, profit-share auctions, experiment |
| JEL: | D44 C92 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:zewdip:327106 |
| By: | Béla Elmshauser; Evan Friedman; Yoon Joo Jo |
| Abstract: | Conveying private information to interested parties is central to almost every economic and social activity. In such interactions, the sender may lie by misreporting the truth, but may also deceive by inducing inaccurate beliefs about the payoff-relevant state. While a huge experimental literature documents aversion to lying, there is little evidence regarding aversion to deceiving others. Deception aversion is conceptually difficult to document because it depends on unobserved second-order beliefs: the sender’s belief over the receiver’s belief (over the payoff-relevant state). In this paper, we introduce a novel game and show theoretically how to identify deception aversion from choice data alone, with minimal assumptions on second-order beliefs. We run a laboratory experiment and find strong support for deception aversion that is robust to several natural variations of the game. Many subjects lie in order to avoid deception, and structural estimates imply that 30% of subjects are deception-averse. |
| Keywords: | lying, deception, lying aversion, deception aversion, image concerns, strategic communication, psychological game theory |
| JEL: | C44 C72 C92 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12154 |
| By: | Dong, Xiaoge (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We study “willful ignorance” - choosing not to learn whether a task is illegal - in a lawmaker-principal-agent game and characterize the penalty policies that implement welfare-maximizing behavior. The model delivers an implementability frontier : which equilibrium behaviors can exist and be selected by penalties. With perfect inquiry, this frontier is aligned with the welfare ordering, so the lawmaker can make the welfare-maximizing behavior both exist and be preferred by all parties. With imperfect inquiry, noise breaks that alignment and produces two failures: inquiry that is socially desirable may be infeasible at any penalty, and inquiry that is socially undesirable may persist because it cannot be switched off. We compare harm-based, compliance-based, and dual-penalty rules: harm-based rules preserve control but tightens feasibility; compliance-based rules relax feasibility but sacrifices control; dual penalty rules recover both levers subject to simple bounds. The framework yields practical guidance for calibrating penalties to harm, inquiry accuracy, and inquiry costs. It also implies that ignorance cannot serve as a shield: the absence of knowing crime in equilibrium is driven by incentives rather than morality, making non-inquiry the true strategic margin of liability design |
| Keywords: | willful ignorance, ostrich instruction, law and economics, asymmetric information. |
| Date: | 2025–09–26 |
| URL: | https://d.repec.org/n?u=RePEc:bie:wpaper:752 |
| By: | Ganglmair, Bernhard; Klix, Julian; Shin, Dongsoo |
| Abstract: | Many business relationships begin with informal interactions and later transition to formal contracts. Using a repeated-games model with a finite horizon, we show that this hybrid-contracting approach can both prolong cooperation (intensive margin) and enable it across a broader range of settings (extensive margin). We model the contract as a "smooth-landing contract" that limits actions only near the end of the relationship. We show that this flexible design supports early cooperation and outperforms rigid contracts. Our findings are robust to changes in contracting costs and timing, with optimal contract length balancing profitability and implementability. |
| Keywords: | cooperation, hybrid contracting, relational contracts, repeated games, strategic alliances |
| JEL: | C73 D86 K12 L14 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:zewdip:327114 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a dynamic theory of contracting with one principal and many agents, extending the promised-utility framework of Sannikov (2008) to environments with competition, correlated outputs, and relative performance evaluation (RPE). We show that the first-order approach remains valid when the principal filters performance through generalized least squares (GLS) residuals of peer outputs, which minimize variance while preserving incentive slopes. The principal's Hamilton- Jacobi-Bellman equation links optimal effort to three forces: marginal revenue, signal informativeness, and intertemporal insurance. In a linear-quadratic environment, equilibrium effort is uniquely determined by a contraction mapping, resolving the multiplicity of equilibria found in static models such as Mookherjee (1984). We further unify Lazear-Rosen (1981) tournaments and linear RPE contracts as diffusion-driven special cases - Gaussian, CIR, and lognormal - within a mean field game system. The framework rationalizes empirical puzzles in executive pay, sales contests, and financial benchmarking, and generates new testable predictions about incentives and organizational scale. |
| Keywords: | Dynamic contracts; Principal-agent problem; Multi-agent incentives; Relative performance evaluation; Tournaments; Mean field games; Hamilton-Jacobi-Bellman equation; Fokker-Planck dynamics; Incentives and insurance; Executive compensation; Organizational design |
| Date: | 2025–09–19 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:791 |
| By: | Benndorf, Volker; Kübler, Dorothea; Normann, Hans-Theo |
| Abstract: | Information unraveling is an elegant theoretical argument suggesting that private information is voluntarily and fully revealed in many circumstances. However, the experimental literature has documented many cases of incomplete unraveling and has suggested limited depth of reasoning on the part of senders as a behavioral explanation. To test this explanation, we modify the design of existing unraveling games along two dimensions. In contrast to the baseline setting with simultaneous moves, we introduce a variant where decision-making is essentially sequential. Second, we vary the cost of disclosure, resulting in a 2×2 treatment design. Both sequential decision-making and low disclosure costs are suitable for reducing the demands on subjects' level-k reasoning. The data confirm that sequential decision-making and low disclosure costs lead to more disclosure, and there is virtually full disclosure in the treatment that combines both. A calibrated level-k model makes quantitative predictions, including precise treatment level and player-specific revelation rates, and these predictions organize the data well. The timing of decisions provides further insights into the treatment-specific unraveling process. |
| Keywords: | information revelation, level-k reasoning, sequential decisions, calibration |
| JEL: | C72 C90 C91 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:dicedp:327129 |
| By: | Francesc Dilmé; Aaron Kolb |
| Abstract: | We revisit the classic chain-store paradox by introducing a novel element: the arrival of exogenous, public signals about the incumbent’s private type over time. As the horizon lengthens, two opposing forces come into play. On one hand, standard reputational incentives grow stronger; on the other, the increasing availability of information makes it more difficult to sustain a reputation. We show that full deterrence can still emerge as the horizon grows arbitrarily long, though not always, and we provide a complete characterization of the conditions under which it arises. |
| Keywords: | Entry deterrence, reputation, chain-store parardox |
| JEL: | C72 C73 |
| Date: | 2025–10 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_704 |
| By: | Heng-fu Zou |
| Abstract: | We analyze a continuum of risk-neutral agents working under a risk-neutral principal. Each agent's output depends on hidden effort and random shocks, while the principal observes both individual outcomes and their cross-sectional average. Agents value consumption linearly but face quadratic effort costs, with all parties discounting at a common rate. We derive the optimal contract in closed form. It consists of a fixed salary plus a relative-performance component that rewards an agent's outcome compared to the group average. This design preserves incentives, since no individual can influence the average, while filtering out common risks and transitory fluctuations. In the unique symmetric equilibrium, all agents exert constant efficient effort, and the fixed salary adjusts to ensure participation. Because of risk neutrality, the contract is independent of the level of randomness. |
| Keywords: | principal-agent problem; mean field games; contract theory; relative performance evaluation; optimal incentives; symmetric equilibrium; risk neutrality |
| Date: | 2025–09–12 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:789 |
| By: | Bolz, Simon J. |
| JEL: | F12 F15 F18 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:vfsc25:325364 |
| By: | Kevin He (University of Pennsylvania); Jonathan Libgober (University of Southern California) |
| Abstract: | We study misperceptions of private-signal correlation in an incomplete-information Cournot duopoly game. Exaggerating the correlation between players’ demand signals is beneficial when agents hold flexible beliefs about price elasticity, but harmful when their beliefs are dogmatically correct. For agents with flexible beliefs who learn elasticity by observing prices, correlation misperceptions indirectly distort behavior through elasticity misinference. If agents know the true elasticity, this learning channel is eliminated. Correlation misperceptions have opposite direct and indirect effects on behavior, so the presence of elasticity inference can reverse an error’s viability. |
| Date: | 2025–08–27 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:25-018 |
| By: | Heng-fu Zou |
| Abstract: | This paper develops a continuous-time model of contracting between a principal and many agents under moral hazard, linking dynamic contract theory to the mean field game(MFG) framework. Outputs depend on effort, competition, and both idiosyncratic and common shocks. The principal designs contracts using filtered signals that benchmark agents against peers. We show that the first-order approach remains valid: effort is linear in exposure with slope determined by the informativeness of fltered outputs. The Hamilton-Jacobi-Bellman equation implies that optimal incentives depend jointly on marginal revenue, signal variance, and intertemporal insurance. The optimal filter is the generalized least squares residual, which asymptotically eliminates common shocks as group size grows. In a linear-quadratic specialization, equilibrium exists, is unique, and is globally stable, with the uniqueness result coinciding with the Lasry-Lions MFG fixed-point condition. The framework unifies tournaments, RPE, and dynamic contracts, and explains empirical puzzles in executive pay, sales teams, and finance. |
| Keywords: | Dynamic contracts; Principal-agent problem; Multi-agent incentives; Relative performance evaluation; Tournaments; Mean field games; Hamilton-Jacobi-Bellman equation; Fokker-Planck dynamics; Incentives and insurance; Executive compensation; Organizational design |
| Date: | 2025–09–10 |
| URL: | https://d.repec.org/n?u=RePEc:cuf:wpaper:790 |
| By: | Ille, Sebastian; Carrera, Edgar J. Sanchez |
| Abstract: | With the increasing demand for sustainable products, greenwashing has become more prevalent and sophisticated over the past decade. To better understand the incentives for firms to greenwash, we develop an evolutionary game-theoretic model in which firms may choose to mimic green behavior without having to bear the cost linked to green investment and production. We provide the conditions for the different evolutionarily stable equilibria. In a second step, we extend the model using agent-based simulations to incorporate path-dependent investment/production costs, history-dependent mimicry effectiveness, peer effects, and localized firm interactions. We show that the simpler model with random matching offers good approximations of the equilibrium conditions in more complex setups, but market segmentation supports green investment and production in contrast to higher penalties. While curtailing opportunities to pretend green behavior boosts green production, we also find that increasing cost efficiencies encourage firms to engage in green production, even in the face of increasingly sophisticated deceptive strategies. Based on our results, we suggest trio-targeted policies that reduce the (initial) costs of green investment/production, curtail opportunities to mimic green behavior, and support segmentation. |
| Keywords: | climate change; non-linear macroeconomic models; greenwashing; corporate sustainability |
| JEL: | C7 D2 Q5 |
| Date: | 2025–08–03 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:126152 |
| By: | Daniel Overbeck; Eliya Lungu |
| Abstract: | This paper shows that bargaining over tax payments is an important feature of tax compliance and enforcement in lower income countries. Analyzing the universe of administrative tax filings from Zambia, we document sharp bunching in (i) dominated regions above tax schedule discontinuities, inconsistent with standard models of tax compliance and (ii) at round number tax payments, implying that certain payments are being targeted. Additional evidence from our own survey suggests that discussing tax payments with tax officials before filing taxes is widespread, in line with tax payments being the outcomes of bargaining. Such bargaining over taxes is consistent with fact (ii), as bargaining outcomes are often round and salient numbers, and with fact (i), because tax schedule discontinuities restrict the set of feasible bargaining outcomes. Finally, we generalize the conventional Allingham & Sandmo (1972) model to allow for bargaining as a mode of tax compliance. We show that bargaining leads to Pareto-improvements for both taxpayers and the state as long as state capacity is sufficiently low. |
| Keywords: | taxation, bargaining, development, small-and medium enterprises, tax compliance, Zambia |
| JEL: | H20 O17 D73 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12172 |
| By: | Schulte, Elisabeth; Friehe, Tim |
| JEL: | K13 L15 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:vfsc25:325372 |