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on Game Theory |
| By: | Andrea Benso |
| Abstract: | We consider a repeated game in which players, considered as nodes of a network, are connected. Each player observes her neighbors' moves only. Thus, monitoring is private and imperfect. Players can communicate with their neighbors at each stage; each player, for any subset of her neighbors, sends the same message to any player of that subset. Thus, communication is local and both public and private. Both communication and monitoring structures are given by the network. The solution concept is perfect Bayesian equilibrium. In this paper we show that a folk theorem holds if and only if the network is 2-connected for any number of players. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.10148 |
| By: | Ran Spiegler |
| Abstract: | Can players sustain long-run trust when their equilibrium beliefs are shaped by machine-learning methods that penalize complexity? I study a game in which an infinite sequence of agents with one-period recall decides whether to place trust in their immediate successor. The cost of trusting is state-dependent. Each player's best response is based on a belief about others' behavior, which is a coarse fit of the true population strategy with respect to a partition of relevant contingencies. In equilibrium, this partition minimizes the sum of the mean squared prediction error and a complexity penalty proportional to its size. Relative to symmetric mixed-strategy Nash equilibrium, this solution concept significantly narrows the scope for trust. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.10363 |
| By: | Volker Nocke; Nicolas Schutz |
| Abstract: | We adopt a potential games approach to study multiproduct-firm pricing games.We introduce the new concept of transformed potential and characterize the classes of demand systems that give rise to pricing games admitting such a potential. The resulting demand systems may contain nests (of closer substitutes) or baskets (of products that are purchased jointly), or combinations thereof. These demand systems allow for flexible substitution patterns, and can feature product complementarities arising from joint purchases and substitution away from the outside option. Combining the potential games approach with a competition-in-utility approach, we derive powerful results on existence of pure-strategy Nash equilibria. |
| Keywords: | Multiproduct firms, potential game, oligopoly pricing, complementary goods, joint purchases, nests |
| JEL: | L13 D43 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_644_v2 |
| By: | Zihao Li |
| Abstract: | We study a model of dynamic monopoly with differentiated goods that buyers can freely dispose of. The model extends the framework of Coasian bargaining to situations in which the quantity or quality of the good is endogenously determined. Our main result is that when players are patient, the seller can sustain in equilibrium any payoff between the lowest possible buyer valuation and (approximately) the highest payoff achievable with commitment power, thus establishing a folk theorem. We apply our model to data markets, where data brokers sell marketing lists to producers. Methodologically, we leverage the connection between sequential bargaining and static mechanism design. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.13137 |
| By: | Mohammed Alsobay; David G. Rand; Duncan J. Watts; Abdullah Almaatouq |
| Abstract: | Punishment as a mechanism for promoting cooperation has been studied extensively for more than two decades, but its effectiveness remains a matter of dispute. Here, we examine how punishment's impact varies across cooperative settings through a large-scale integrative experiment. We vary 14 parameters that characterize public goods games, sampling 360 experimental conditions and collecting 147, 618 decisions from 7, 100 participants. Our results reveal striking heterogeneity in punishment effectiveness: while punishment consistently increases contributions, its impact on payoffs (i.e., efficiency) ranges from dramatically enhancing welfare (up to 43% improvement) to severely undermining it (up to 44% reduction) depending on the cooperative context. To characterize these patterns, we developed models that outperformed human forecasters (laypeople and domain experts) in predicting punishment outcomes in new experiments. Communication emerged as the most predictive feature, followed by contribution framing (opt-out vs. opt-in), contribution type (variable vs. all-or-nothing), game length (number of rounds), peer outcome visibility (whether participants can see others' earnings), and the availability of a reward mechanism. Interestingly, however, most of these features interact to influence punishment effectiveness rather than operating independently. For example, the extent to which longer games increase the effectiveness of punishment depends on whether groups can communicate. Together, our results refocus the debate over punishment from whether or not it "works" to the specific conditions under which it does and does not work. More broadly, our study demonstrates how integrative experiments can be combined with machine learning to uncover generalizable patterns, potentially involving interactions between multiple features, and help generate novel explanations in complex social phenomena. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.17151 |
| By: | Grund, Christian (RWTH Aachen University); Monschau, Philipp (RWTH Aachen University) |
| Abstract: | We study the role of purpose-based rules for behavior and outcomes in a threshold public good game. Rules can be sufficient or even inflated in terms of proposing a fulfilling behavior. We conduct a lab experiment to describe the implications caused by the inflation of a rule. Our study shows that inflated rules are obeyed less. Yet, rule-following occurs also with inflated rules which leads to lower efficiency regarding exactly providing the threshold. A fair share option can help to coordinate efficiently. We complement our analysis by the investigation of the role of the implemented rules for the ex-post optimal behavior, i.e. evaluating the individual contribution depending on the individual payoff. |
| Keywords: | thresholds, groups, cooperation, coordination, rule-following, public goods |
| JEL: | C9 H41 M5 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp18075 |
| By: | Yaron Azrieli; Rachana Das |
| Abstract: | We study a model of persuasion in which the receiver is a `conservative Bayesian' whose updated belief is a convex combination of the prior and the correct Bayesian posterior. While in the classic Bayesian case providing information sequentially is never valuable, we show that the sender gains from sequential persuasion in many of the environments considered in the literature on strategic information transmission. We also consider the case in which the sender and receiver are both biased and prove that the maximal expected payoff for the sender under sequential persuasion is the same as in the case where neither of them is biased. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.09464 |
| By: | Asen Kochov; Yangwei Song |
| Abstract: | We study infinitely repeated games in which the players’ rates of time preference may evolve endogenously in the course of the game. Our goal is to strengthen the folk theorem of Kochov and Song (2023) by relaxing the assumption of observable mixtures. To that end, we identify and impose a new sufficient condition on preferences. The condition holds automatically in the standard case of time-separable utilities and a common discount factor, while being generic in ours. |
| Keywords: | folk theorem, recursive utility, endogenous discounting, unobserved mixtures |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_12066 |
| By: | Maxwell Rosenthal |
| Abstract: | This paper develops a data-driven approach to Bayesian persuasion. The receiver is privately informed about the prior distribution of the state of the world, the sender knows the receiver's preferences but does not know the distribution of the state variable, and the sender's payoffs depend on the receiver's action but not on the state. Prior to interacting with the receiver, the sender observes the distribution of actions taken by a population of decision makers who share the receiver's preferences in best response to an unobserved distribution of messages generated by an unknown and potentially heterogeneous signal. The sender views any prior that rationalizes this data as plausible and seeks a signal that maximizes her worst-case payoff against the set of all such distributions. We show positively that the two-state many-action problem has a saddle point and negatively that the two-action many-state problem does not. In the former case, we identify adversarial priors and optimal signals. In the latter, we characterize the set of robustly optimal Blackwell experiments. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.03203 |
| By: | Jonathan Bendor; Lukas Bolte; Nicole Immorlica; Matthew O. Jackson |
| Abstract: | It is socially beneficial for teams to cooperate in some situations (``good games'') and not in others (``bad games;'' e.g., those that allow for corruption). A team's cooperation in any given game depends on expectations of cooperation in future iterations of both good and bad games. We identify when sustaining cooperation on good games necessitates cooperation on bad games. We then characterize how a designer should optimally assign workers to teams and teams to tasks that involve varying arrival rates of good and bad games. Our results show how organizational design can be used to promote cooperation while minimizing corruption. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.03030 |
| By: | Olivier Bos; Nicolas Fugger; Sander Onderstal |
| 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:ces:ceswps:_12071 |
| By: | Hiroto Sato; Konan Shimizu |
| Abstract: | In social learning environments, agents acquire information from both private signals and the observed actions of predecessors, referred to as history. We define the value of history as the gain in expected payoff from accessing both the private signal and history, compared to relying on the signal alone. We first characterize the information structures that maximize this value, showing that it is highest under a mixture of full information and no information. We then apply these insights to a model of markets for history, where a monopolistic data seller collects and sells access to history. In equilibrium, the seller's dynamic pricing becomes the value of history for each agent. This gives the seller incentives to increase the value of history by designing the information structure. The seller optimal information discloses less information than the socially optimal level. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.11029 |
| By: | Georgy Lukyanov; Samuel Safaryan |
| Abstract: | We study public persuasion when a sender faces a mass audience that can verify the state at heterogeneous costs. The sender commits ex ante to a public information policy but must satisfy an ex post truthfulness constraint on verifiable content (EPIC). Receivers verify selectively, generating a verifying mass that depends on the public posterior mu. This yields an indirect value v(mu;F) and a concavification problem under implementability. Our main result is a reverse comparative static: when verification becomes cheaper (an FOSD improvement in F), v becomes more concave and the optimal public signal is strictly less informative (Blackwell). Intuitively, greater verifiability makes extreme claims invite scrutiny, so the sender optimally coarsens information - "confusion as strategy." We extend the model to two ex post instruments: falsification (continuous manipulation) and violence (a fixed-cost discrete tool), and characterize threshold substitutions from persuasion to manipulation and repression. The framework speaks to propaganda under improving fact-checking. |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2508.19682 |
| By: | Marina Agranov; S. Nageeb Ali; B. Douglas Bernheim; Thomas R. Palfrey |
| Abstract: | Strategic models of legislative bargaining predict that proposers can extract high shares of economic surplus by identifying and exploiting weak coalition partners. However, strength and weakness can be difficult to assess even with relatively simple bargaining protocols. We evaluate experimentally how strategic complexity affects the ability to identify weak coalition partners, and for the partners themselves to determine whether their positions are weak or strong. We find that, as strategic complexity progressively obscures bargaining strength, proposers migrate to egalitarianism, in significant part because non-proposers begin placing substantial weight on fairness. Greater analytic skill dampens but does not eliminate these patterns. |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2507.15682 |
| By: | Yu-Jui Huang; Shihao Zhu |
| Abstract: | This paper considers two investors who perform mean-variance portfolio selection with asymmetric information: one knows the true stock dynamics, while the other has to infer the true dynamics from observed stock evolution. Their portfolio selection is interconnected through relative performance concerns, i.e., each investor is concerned about not only her terminal wealth, but how it compares to the average terminal wealth of both investors. We model this as Stackelberg competition: the partially-informed investor (the "follower") observes the trading behavior of the fully-informed investor (the "leader") and decides her trading strategy accordingly; the leader, anticipating the follower's response, in turn selects a trading strategy that best suits her objective. To prevent information leakage, the leader adopts a randomized strategy selected under an entropy-regularized mean-variance objective, where the entropy regularizer quantifies the randomness of a chosen strategy. The follower, on the other hand, observes only the actual trading actions of the leader (sampled from the randomized strategy), but not the randomized strategy itself. Her mean-variance objective is thus a random field, in the form of an expectation conditioned on a realized path of the leader's trading actions. In the idealized case of continuous sampling of the leader's trading actions, we derive a Stackelberg equilibrium where the follower's trading strategy depends linearly on the actual trading actions of the leader and the leader samples her trading actions from Gaussian distributions. In the realistic case of discrete sampling of the leader's trading actions, the above becomes an $\epsilon$-Stackelberg equilibrium. |
| Date: | 2025–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2509.03669 |
| By: | Christoph Carnehl; Anton Sobolev; Konrad Stahl; André Stenzel |
| Abstract: | We study information design in a vertically differentiated market. Two firms offer products of ex-ante unknown qualities. A third party designs a system to publicly disclose information. More precise information guides consumers toward their preferred product but increases expected product differentiation, allowing firms to raise prices. Full disclosure of the product ranking alone suffices to maximize industry profits. Consumer surplus is maximized, however, whenever no information about the product ranking is disclosed, as the benefit of competitive pricing always dominates the loss from suboptimal choices. The provision of public information on product quality becomes questionable. |
| Keywords: | Information Design, Vertical Product Differentiation, Quality Rankings, Competition |
| JEL: | D43 D82 L13 L15 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2025_700 |
| By: | Dmitry Aldokhin (Bank of Russia, Russian Federation); Anton Belyakov (Bank of Russia, Russian Federation Author-Name: Elena Deryugina Author-Email: DeryuginaEB@cbr.ru Author-Workplace-Name: Bank of Russia, Russian Federation Author-Name: Alexey Ponomarenko Author-Email: PonomarenkoAA@cbr.ru Author-Workplace-Name: Bank of Russia, Russian Federation) |
| Abstract: | We model the deposit market, where commercial banks compete using deposit interest rates, and depositors initially distributed among banks, when switching to another bank, bear the exogenous switching costs associated with a lack of information and money transfer fee. We consider both discrete and continuous distribution of depositors over switching costs and find equilibria in pure strategies. The theoretical model in hand allows us to explain the empirically observed negative relation between the size of a bank and its weighted average deposit rate. We show that this dependence may be the result of the history of the banking market formation. Initially, established banks could manage to obtain a majority of depositors with high switching costs, while depositors with low costs could be lost to newly emerging banks. Because of this, previously established banks can set lower deposit rates without fear that their depositors will switch to competitors, and maintain a large share of all depositors in the market. It follows from the analysis that the division of large banks into smaller ones will not lead to an increase in their deposit interest rates, but on the contrary, may even increase discrimination against depositors with high transition costs. It is the reduction of depositors’ switching costs that makes banks to raise deposit rates and thus increase public welfare. |
| Keywords: | : banks, deposits, switching costs, Nash equilibrium, equilibrium in secure strategies, welfare |
| JEL: | D42 D43 D60 E58 G21 L13 |
| Date: | 2025–07 |
| URL: | https://d.repec.org/n?u=RePEc:bkr:wpaper:wps151 |
| By: | Simon Finster (FAIRPLAY - IA coopérative : équité, vie privée, incitations - CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - IP Paris - Institut Polytechnique de Paris - Criteo AI Lab - Criteo [Paris] - Centre Inria de l'Institut Polytechnique de Paris - Centre Inria de Saclay - Inria - Institut National de Recherche en Informatique et en Automatique); Patrick Loiseau (FAIRPLAY - IA coopérative : équité, vie privée, incitations - CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - IP Paris - Institut Polytechnique de Paris - Criteo AI Lab - Criteo [Paris] - Centre Inria de l'Institut Polytechnique de Paris - Centre Inria de Saclay - Inria - Institut National de Recherche en Informatique et en Automatique); Simon Mauras (FAIRPLAY - IA coopérative : équité, vie privée, incitations - CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - IP Paris - Institut Polytechnique de Paris - Criteo AI Lab - Criteo [Paris] - Centre Inria de l'Institut Polytechnique de Paris - Centre Inria de Saclay - Inria - Institut National de Recherche en Informatique et en Automatique); Mathieu Molina (FAIRPLAY - IA coopérative : équité, vie privée, incitations - CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - GENES - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - GENES - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique - IP Paris - Institut Polytechnique de Paris - Criteo AI Lab - Criteo [Paris] - Centre Inria de l'Institut Polytechnique de Paris - Centre Inria de Saclay - Inria - Institut National de Recherche en Informatique et en Automatique); Bary Pradelski (MFO - Maison Française d'Oxford - MEAE - Ministère de l'Europe et des Affaires étrangères - CNRS - Centre National de la Recherche Scientifique, LIG - Laboratoire d'Informatique de Grenoble - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes, POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems - Centre Inria de l'Université Grenoble Alpes - Inria - Institut National de Recherche en Informatique et en Automatique - LIG - Laboratoire d'Informatique de Grenoble - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes) |
| Abstract: | We initiate the study of how auction design affects the division of surplus among buyers. We propose a parsimonious measure for equity and apply it to the family of standard auctions for homogeneous goods. Our surplus-equitable mechanism is efficient, Bayesian-Nash incentive compatible, and achieves surplus parity among winners ex-post. The uniform-price auction is equity-optimal if and only if buyers have a pure common value. Against intuition, the pay-as-bid auction is not always preferred in terms of equity if buyers have pure private values. In auctions with price mixing between pay-as-bid and uniform prices, we provide prior-free bounds on the equity-preferred pricing rule under a common regularity condition on signals. |
| Keywords: | uniform price, pay-as-bid, mechanism design, equity, auctions, common value |
| Date: | 2025–07–07 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05225702 |
| By: | William A. Brock; Bo Chen; Steven N. Durlauf; Shlomo Weber |
| Abstract: | This paper analyzes patterns of majority language acquisition in an economy consisting of a majority group and multiple minority groups. We consider contexts in which allows individuals choose among three options: full learning, partial learning, or no learning of the majority language. The key innovation in our approach is the introduction of a conformity factor in language acquisition, where peer pressure and community status may outweigh communicative and economic incentives for some individuals. Notably, we identify a non-monotonic relationship between the level of conformity and the distribution of full learners, partial learners, and non-learners in equilibrium. This finding is significant for policy considerations, as small adjustments in language acquisition costs may unpredictably influence language acquisition patterns across minority groups. |
| JEL: | C72 D61 J15 Z13 |
| Date: | 2025–08 |
| URL: | https://d.repec.org/n?u=RePEc:nbr:nberwo:34138 |