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on Game Theory |
| By: | Yu Gui; Bahar Ta\c{s}kesen |
| Abstract: | We introduce the Statistical Equilibrium of Optimistic Beliefs (SE-OB) for the mixed extension of finite normal-form games, drawing insights from discrete choice theory. Departing from the conventional best responders of Nash equilibrium and the better responders of quantal response equilibrium, we reconceptualize player behavior as that of optimistic better responders. In this setting, the players assume that their expected payoffs are subject to random perturbations, and form optimistic beliefs by selecting the distribution of perturbations that maximizes their highest anticipated payoffs among belief sets. In doing so, SE-OB subsumes and extends the existing equilibria concepts. The player's view of the existence of perturbations in their payoffs reflects an inherent risk sensitivity, and thus, each player is equipped with a risk-preference function for every action. We demonstrate that every Nash equilibrium of a game, where expected payoffs are regularized with the risk-preference functions of the players, corresponds to an SE-OB in the original game, provided that the belief sets coincide with the feasible set of a multi-marginal optimal transport problem with marginals determined by risk-preference functions. Building on this connection, we propose an algorithm for repeated games among risk-sensitive players under optimistic beliefs when only zeroth-order feedback is available. We prove that, under appropriate conditions, the algorithm converges to an SE-OB. Our convergence analysis offers key insights into the strategic behaviors for equilibrium attainment: a player's risk sensitivity enhances equilibrium stability, while forming optimistic beliefs in the face of ambiguity helps to mitigate overly aggressive strategies over time. As a byproduct, our approach delivers the first generic convergent algorithm for general-form structural QRE beyond the classical logit-QRE. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.09569 |
| By: | Fabio A. C. C. Chalub; Max O. Souza |
| Abstract: | Real populations are seldom found at the Nash equilibrium strategy. The present work focuses on how population size can be a relevant evolutionary force diverting the population from its expected Nash equilibrium. We introduce the concept of insuperable strategy, a strategy that guarantees that no other player can have a larger payoff than the player that adopts it. We show that this concept is different from the rationality assumption frequently used in game theory and that for small populations the insuperable strategy is the most probable evolutionary outcome for any dynamics that equal game payoff and reproductive fitness. We support our ideas with several examples and numerical simulations. We finally discuss how to extend the concept to multiplayer games, introducing, in a limited way, the concept of game reduction. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.07652 |
| By: | Frederic Koessler; Marco Scarsini; Tristan Tomala |
| Abstract: | This paper studies the implementation of Bayes correlated equilibria in symmetric Bayesian nonatomic games, using direct information structures and obedient strategies. The main results demonstrate full implementation in a class of games with positive cost externalities. Specifically, if the game admits a strictly convex potential in every state, then for every Bayes correlated equilibrium outcome with finite support and rational action distributions, there exists a direct information structure that implements this outcome under all equilibria. When the potential is only weakly convex, we show that all equilibria implement the same expected social cost. Additionally, all Bayes correlated equilibria, including those with infinite support or irrational action distributions, are approximately implemented. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.05920 |
| By: | Raj Pabari; Udaya Ghai; Dominique Perrault-Joncas; Kari Torkkola; Orit Ronen; Dhruv Madeka; Dean Foster; Omer Gottesman |
| Abstract: | We introduce and analyze a variation of the Bertrand game in which the revenue is shared between two players. This game models situations in which one economic agent can provide goods/services to consumers either directly or through an independent seller/contractor in return for a share of the revenue. We analyze the equilibria of this game, and show how they can predict different business outcomes as a function of the players' costs and the transferred revenue shares. Importantly, we identify game parameters for which independent sellers can simultaneously increase the original player's payoff while increasing consumer surplus. We then extend the shared-revenue Bertrand game by considering the shared revenue proportion as an action and giving the independent seller an outside option to sell elsewhere. This work constitutes a first step towards a general theory for how partnership and sharing of resources between economic agents can lead to more efficient markets and improve the outcomes of both agents as well as consumers. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.07952 |
| By: | Kyung Hwan Baik; Dongwoo Lee |
| Abstract: | We study contests in which two groups compete to win (or not to win) a group-specific public-good/bad prize. Each player in the groups can exert two types of effort: one to help her own group win the prize, and one to sabotage her own group's chances of winning it. The players in the groups choose their effort levels simultaneously and independently. We introduce a specific form of contest success function that determines each group's probability of winning the prize, taking into account players' sabotage activities. We show that two types of purestrategy Nash equilibrium occur, depending on parameter values: one without sabotage activities and one with sabotage activities. In the first type, only the highest-valuation player in each group expends positive effort, whereas, in the second type, only the lowest-valuation player in each group expends positive effort. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.08100 |
| By: | Shengyuan Huang; Wenjun Mei; Xiaoguang Yang; Zhigang Cao |
| Abstract: | This paper studies allocation mechanisms in max-flow games with players' capacities as private information. We first show that no core-selection mechanism is truthful: there may exist a player whose payoff increases if she under-reports her capacity when a core-section mechanism is adopted. We then introduce five desirable properties for mechanisms in max-flow games: DSIC (truthful reporting is a dominant strategy), SIR (individual rationality and positive payoff for each player contributing positively to at least one coalition), SP (no edge has an incentive to split into parallel edges), MP (no parallel edges have incentives to merge), and CM (a player's payoff does not decrease as another player's capacity and max-flow increase). While the Shapley value mechanism satisfies DSIC and SIR, it fails to meet SP, MP and CM. We propose a new mechanism based on minimal cuts that satisfies all five properties. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.08248 |
| By: | Harry Pei |
| Abstract: | Each period, two players bargain over a unit of surplus. Each player chooses between remaining flexible and committing to a take-it-or-leave-it offer at a cost. If players' committed demands are incompatible, then the current-period surplus is destroyed in the conflict. When both players are flexible, the surplus is split according to the status quo, which is the division in the last period where there was no conflict. We show that when players are patient and the cost of commitment is small, there exist a class of symmetric Markov Perfect equilibria that are asymptotically efficient and renegotiation proof, in which players commit to fair demands in almost all periods. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.01053 |
| By: | Kensei Nakamura |
| Abstract: | In Nash's (1950) seminal result, independence of irrelevant alternatives (IIA) plays a central role, but it has long been a subject of criticism in axiomatic bargaining theory. This paper examines the implication of a weak version of IIA in multi-valued bargaining solutions defined on non-convex bargaining problems. We show that if a solution satisfies weak IIA together with standard axioms, it can be represented, like the Nash solution, using weighted products of normalized utility levels. In this representation, the weight assigned to players for evaluating each agreement is determined endogenously through a two-stage optimization process. These solutions bridge the two dominant solution concepts, the Nash solution and the Kalai-Smorodinsky solution (Kalai and Smorodinsky, 1975). Furthermore, we consider special cases of these solutions in the context of bargaining over linear production technologies. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.06157 |
| By: | Steven Kivinen; Christoph Kuzmics |
| Abstract: | An informed Advisor and an uninformed Decision-Maker engage in repeated cheap talk communication in always new (stochastically independent) decision problems. They have a conflict of interest over which action should be implemented at least in some cases. Our main result is that, while the Decision-Maker's optimal payoff is attainable in some subgame perfect equilibrium (by force of the usual folk theorem), no payoff profile close to the Decision-Maker's optimal one is immune to renegotiation. Pareto efficient renegotiation-proof equilibria are typically attainable, and they entail a compromise between the Advisor and the Decision-Maker. This could take the form of the Advisor being truthful and the Decision-Maker not utilizing this information to their own full advantage, or the Advisor being somewhat liberal with the truth and the Decision-Maker, while fully aware of this, pretending to believe the Advisor. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.08296 |
| By: | Gaël Thébaud (UMR PHIM - Plant Health Institute of Montpellier - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - IRD - Institut de Recherche pour le Développement - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier); César Martinez (BioSP - Biostatistique et Processus Spatiaux - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier); Mabell Tidball (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier); Pierre Courtois (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier) |
| Abstract: | Most plant disease epidemics spread both within and between farms. However, in the absence of collective action, each farmer generally takes disease control decisions based on personal costs and benefits. It is important to identify under which conditions the combination of such private control decisions can have synergistic or antagonistic effects, and can lead to collective economic inefficiencies. We used the game theory framework to investigate these questions, considering a simplified two-period game where two farmers decide whether or not to control an epidemic on their farm. Taking the example of sharka epidemics, caused by plum pox virus in Prunus orchards, we characterized the game and its outcomes according to initial epidemic conditions and focused on those likely to produce economic inefficiencies. Our results show that depending on the initial infection levels, a broad range of games may arise, some of which involving synergistic or antagonistic control decisions. This means that the nature of strategic interactions between famers may change depending on the state of the epidemic. After a thorough characterization of the epidemic conditions for which private management produces collective economic inefficiencies, we investigated the expected effect of different public policy incentives aiming to reduce such inefficiencies. |
| Keywords: | Epidemiology, Economics, Strategy, Collective action, Plum pox virus |
| Date: | 2025–01–19 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-04957505 |
| By: | Nizar Riane |
| Abstract: | This paper examines the recent reform of Morocco's public procurement market through the lens of Keynesian beauty contest theory. The reform introduces a mechanism akin to a guessing-the-average game, where bidders attempt to estimate a reference price, which in turn impacts bidding strategies. We utilize this setup to empirically test key hypotheses within auction theory, specifically the roles of common knowledge and bounded rationality. Our findings indicate potential manipulation risks under the current rules, suggesting that a shift to a median criterion could improve robustness and reduce the likelihood of manipulation. This work contributes to the broader understanding of strategic interactions in procurement and offers a foundation for future research on improving fairness and efficiency in public contract allocation. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.00883 |
| By: | Shitong Wang |
| Abstract: | This paper revisits the limitations of the Median Voter Theorem and introduces a novel framework to analyze the optimal economic ideological positions of political parties. By incorporating Nash equilibrium, we examine the mechanisms and elasticity of ideal deviation costs, voter distribution, and policy feasibility. Our findings show that an increase in a party's ideal deviation cost shifts its optimal ideological position closer to its ideal point. Additionally, if a voter distribution can be expressed as a positive linear combination of two other distributions, its equilibrium point must lie within the interval defined by the equilibrium points of the latter two. We also find that decreasing feasibility costs incentivize governments, regardless of political orientation, to increase fiscal expenditures (e.g., welfare) and reduce fiscal revenues (e.g., taxes). This dynamic highlights the fiscal pressures commonly faced by democratic nations under globalization. Moreover, we demonstrate that even with uncertain voter distributions, parties can identify optimal ideological positions to maximize their utility. Lastly, we explain why the proposed framework cannot be applied to community ideologies due to their fundamentally different nature. This study provides new theoretical insights into political strategies and establishes a foundation for future empirical research. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.06562 |
| By: | Matthew Stephenson; Andrew Miller; Xyn Sun; Bhargav Annem; Rohan Parikh |
| Abstract: | We study a fundamental challenge in the economics of innovation: an inventor must reveal details of a new idea to secure compensation or funding, yet such disclosure risks expropriation. We present a model in which a seller (inventor) and buyer (investor) bargain over an information good under the threat of hold-up. In the classical setting, the seller withholds disclosure to avoid misappropriation, leading to inefficiency. We show that trusted execution environments (TEEs) combined with AI agents can mitigate and even fully eliminate this hold-up problem. By delegating the disclosure and payment decisions to tamper-proof programs, the seller can safely reveal the invention without risking expropriation, achieving full disclosure and an efficient ex post transfer. Moreover, even if the invention's value exceeds a threshold that TEEs can fully secure, partial disclosure still improves outcomes compared to no disclosure. Recognizing that real AI agents are imperfect, we model "agent errors" in payments or disclosures and demonstrate that budget caps and acceptance thresholds suffice to preserve most of the efficiency gains. Our results imply that cryptographic or hardware-based solutions can function as an "ironclad NDA, " substantially mitigating the fundamental disclosure-appropriation paradox first identified by Arrow (1962) and Nelson (1959). This has far-reaching policy implications for fostering R&D, technology transfer, and collaboration. |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2502.07924 |
| By: | Ockenfels, Axel; Gallier, Carlo; Sturm, Bodo |
| Abstract: | International climate negotiations have so far failed to produce ambitious climate cooperation. We combine laboratory experiments with simulations to investigate the performance of two negotiation design features to address this failure: The Paris Agreement's ratchet-up mechanism, which requires countries to gradually increase their ambition, and a new policy proposal to negotiate more frequently. We find that more frequent interactions allow subjects to build trust and cooperation more safely over time. Conversely, subjects in a ratchet-up design tend to become more cautious to protect themselves from free riders. Thus, more frequent revisions of commitments promote cooperation, but the ratchet-up design fails to achieve the same result. |
| Keywords: | Climate change, climate negotiations, cooperation, laboratory experiments, simulations |
| JEL: | C72 C91 C92 D02 H41 Q54 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:zewdip:312184 |
| By: | Arne Lauber; Christoph March; Marco Sahm |
| Abstract: | We conduct a laboratory experiment to compare the fairness and intensity of round-robin tournaments with three symmetric players, a single prize, and two alternative match formats. Matches are either organized as lottery contests or all-pay auctions. Whereas we confirm the theoretical prediction that tournaments are less fair if matches are organized as all-pay auctions, we reject the predicted difference in tournament intensity. Moreover, the reason for the reduced fairness of tournaments based on all-pay auctions is also at odds with theory. In the lab, such tournaments heavily disfavor (in payoff-terms) the player acting in the final two matches. The reason is the substantially weaker than predicted discouragement of this player when competing first against the loser of the first match. Subjects try to exploit a perceived negative psychological momentum in such situations but only manage to end up in a dissipation trap: an effort-intense, final-like last match which significantly reduces their payoffs. |
| Keywords: | sequential round-robin tournaments, lottery contest, all-pay auction, laboratory experiment, discouragement effect, dissipation trap |
| JEL: | C72 C91 D72 Z20 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11677 |