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on Game Theory |
| By: | Florian Ederer; Weicheng Min |
| Abstract: | How does lie detection constrain the potential for one person to persuade another to change her action? We consider a model of Bayesian persuasion in which the Receiver can detect lies with positive probability. We show that the Sender lies more when the lie detection probability increases. As long as this probability is sufficiently small, the Sender's and the Receiver's equilibrium payoffs are unaffected by the presence of lie detection because the Sender simply compensates by lying more. However, when the lie detection probability is sufficiently high, the Sender's equilibrium payoff decreases and the Receiver's equilibrium payoff increases with the lie detection probability. |
| JEL: | D72 D82 D83 K40 M31 |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:30065&r= |
| By: | Erhao Xie |
| Abstract: | In the literature that estimates discrete games with incomplete information, researchers usually impose two assumptions. First, either the payoff function or the distribution of private information or both are restricted to follow some parametric functional forms. Second, players’ behaviors are assumed to be consistent with the Bayesian Nash equilibrium. This paper jointly relaxes both assumptions. The framework non-parametrically specifies both the payoff function and the distribution of private information. In addition, each player’s belief about other players’ behaviors is also modeled as a nonparametric function. I allow this belief function to be any probability distribution over other players’ action sets. This specification nests the equilibrium assumption when each player’s belief corresponds to other players’ actual choice probabilities. It also allows non-equilibrium behaviors when some players’ beliefs are biased or incorrect. Under the above framework, this paper first derives a testable implication of the equilibrium condition. It then obtains the identification results for the payoff function, the belief function and the distribution of private information. |
| Keywords: | Econometric and statistical methods |
| JEL: | C57 |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:bca:bocawp:22-22&r= |
| By: | Saish Nevrekar |
| Abstract: | This paper studies the problem of endogenous coalition formation in contests: how players organize themselves in groups when faced with the common objective of securing a prize by exerting costly effort. The model presented adopts an axiomatic approach by assuming certain properties for the winning probability that imply efficiency gains from cooperation in contest settings. Efficiency gains are said to be generated if any coalition experiences increasing marginal returns with aggregate effort until a threshold. These properties identify a wide class of generalised Tullock contest success functions. We analyse a sequential coalition formation game for an arbitrary number of symmetric players and exogenous effort. If coalitions generate sufficient efficiency gains, then any equilibrium always consists of two or more coalitions where at least two coalitions are of unequal size. This result extends to endogenous efforts if the cost functions are sufficiently convex. |
| Keywords: | Noncooperative games, coalition formation, contest success function |
| JEL: | C72 D74 |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:412&r= |
| By: | Aroon Narayanan |
| Abstract: | I study a game of strategic exploration with private payoffs and public actions in a Bayesian bandit setting. In particular, I look at cascade equilibria, in which agents switch over time from the risky action to the riskless action only when they become sufficiently pessimistic. I show that these equilibria exist under some conditions and establish their salient properties. Individual exploration in these equilibria can be more or less than the single-agent level depending on whether the agents start out with a common prior or not, but the most optimistic agent always underexplores. I also show that allowing the agents to write enforceable ex-ante contracts will lead to the most ex-ante optimistic agent to buy all payoff streams, providing an explanation to the buying out of smaller start-ups by more established firms. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.06107&r= |
| By: | Raouf Boucekkine (ESC Rennes School of Business - ESC Rennes School of Business); Carmen Camacho (PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Weihua Ruan (Purdue University Northwest); Benteng Zou (University of Luxembourg [Luxembourg]) |
| Abstract: | We use a parsimonious two-stage differential game setting where the duration of the first stage, the coalition stage, depends on the will of a particular player to leave the coalition through an explicit timing variable. By specializing in a standard linear-quadratic environmental model augmented with a minimal constitutional setting for the coalition (payoff share parameter), we are able to analytically extract several nontrivial findings. Three key aspects drive the results: the technological gap as an indicator of heterogeneity across players, the constitution of the coalition and the intensity of the public bad (here, the pollution damage). We provide with a full analytical solution to the two-stage differential game. In particular, we characterize the intermediate parametric cases leading to optimal finite time splitting. A key characteristic of these finite-time-lived coalitions is the requirement of the payoff share accruing to the splitting country to be large enough. Incidentally, our two-stage differential game setting reaches the conclusion that splitting countries are precisely those which use to benefit the most from the coalition. Constraining the payoff share to be low by Constitution may lead to optimal everlasting coalitions only provided initial pollution is high enough, which may cover the emergency cases we are witnessing nowadays. |
| Keywords: | Differential games,Multistage optimal control Coalition splitting,environmental agreements,constitutional vs technological heterogeneity,Coalition splitting |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:psewpa:halshs-03676670&r= |
| By: | Saglam, Ismail |
| Abstract: | In this paper, we investigate whether a natural monopoly with private cost information can reduce the likelihood of regulatory threat by investing, in the ex-ante stage, in cost-reducing R&D to generate process innovations and whether such an investment can yield Pareto gains in welfare. We model the regulatory process using a sequential game where a benevolent regulator makes the first move by announcing the probability that the monopolist will be optimally regulated. The monopolist, hearing this announcement, chooses the optimal level of its R&D investment. We numerically compute the subgame-perfect Nash equilibrium of this game for a wide range of model parameters. Our results show that the monopolist invests more in R&D if the regulatory threat is less certain. Anticipating this response, the regulator makes her threat less certain if she puts more weight on the monopolist's welfare. Moreover, we find that regulation with uncertainty can be Pareto superior to regulation with certainty if the welfare weight of the monopolist is sufficiently, but not extremely, high or if the cost of R&D is sufficiently small. |
| Keywords: | Monopoly; regulatory threat, R&D investment. |
| JEL: | D42 D82 L51 O30 |
| Date: | 2022–05–21 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:113155&r= |
| By: | Hendrikse, G.W.J.; Nillson, J. |
| Abstract: | This paper investigates why agricultural cooperatives exhibit different principles for the allocation of decision rights between the Board of Directors and the Management. A mass-action interpretation of the Nash equilibrium in an investment proposal game shows that, on the one hand, board structure variety is an equilibrium outcome while, on the other, the Traditional model (the board has full control) and the Management model (the professional management makes up the Board of the cooperative society) perform better than the Corporation model (the Management is in full control of the cooperative firm). |
| Keywords: | Internal governance, Board of Directors, Management, decision rights, game theory |
| Date: | 2022–05–30 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureri:137123&r= |
| By: | Wanchang Zhang |
| Abstract: | A single unit of a good is sold to one of two bidders. Each bidder has either a high prior valuation or a low prior valuation for the good. Their prior valuations are independently and identically distributed. Each bidder may observe an independently and identically distributed signal about her prior valuation. The seller knows the distribution of the prior valuation profile and knows that signals are independently and identically distributed, but does not know the signal distribution. In addition, the seller knows that bidders play undominated strategies. I find that a second-price auction with a random reserve maximizes the worst-case expected revenue over all possible signal distributions and all equilibria in undominated strategies. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.04137&r= |
| By: | Fupeng Sun; Yanwei Sun; Chiwei Yan; Li Jin |
| Abstract: | By modeling contests as all-pay auctions, we study two-stage sequential elimination contests (SEC) under incomplete information, where only the players with top efforts in the first stage can proceed to the second and final stage to compete for prizes. Players have privately held type/ability information that impacts their costs of exerting efforts. We characterize players' Perfect Bayesian Equilibrium strategies and discover a somewhat surprising result: all players exert weakly lower efforts in the final stage of the SEC compared to those under a one-round contest, regardless of the number of players admitted to the final stage. This result holds under any multi-prize reward structure, any type distribution and cost function. As a consequence, in terms of the expected highest effort or total efforts of the final stage, the optimal SEC is equivalent to a one-round contest by letting all players proceed to the final stage. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.08104&r= |
| By: | Hidemasa Ishii; Nariaki Nishino |
| Abstract: | The literature on centralized matching markets often assumes that a true preference of each player is known to herself and fixed, but empirical evidence casts doubt on its plausibility. To circumvent the problem, we consider evolutionary dynamics of preference revelation games in marriage problems. We formulate the asymptotic stability of a matching, indicating the dynamical robustness against sufficiently small changes in players' preference reporting strategies, and show that asymptotically stable matchings are stable when they exist. The simulation results of replicator dynamics are presented to demonstrate the asymptotic stability. We contribute a practical insight for market designers that a stable matching may be realized by introducing a learning period in which participants find appropriate reporting strategies through trial and error. We also open doors to a novel area of research by demonstrating ways to employ evolutionary game theory in studies on centralized markets. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.08079&r= |
| By: | Nika Haghtalab; Nicole Immorlica; Brendan Lucier; Markus Mobius; Divyarthi Mohan |
| Abstract: | We study a communication game between a sender and receiver where the sender has access to a set of informative signals about a state of the world. The sender chooses one of her signals, called an ``anecdote'' and communicates it to the receiver. The receiver takes an action, yielding a utility for both players. Sender and receiver both care about the state of the world but are also influenced by a personal preference so that their ideal actions differ. We characterize perfect Bayesian equilibria when the sender cannot commit to a particular communication scheme. In this setting the sender faces ``persuasion temptation'': she is tempted to select a more biased anecdote to influence the receiver's action. Anecdotes are still informative to the receiver but persuasion comes at the cost of precision. This gives rise to ``informational homophily'' where the receiver prefers to listen to like-minded senders because they provide higher-precision signals. In particular, we show that a sender with access to many anecdotes will essentially send the minimum or maximum anecdote even though with high probability she has access to an anecdote close to the state of the world that would almost perfectly reveal it to the receiver. In contrast to the classic Crawford-Sobel model, full revelation is a knife-edge equilibrium and even small differences in personal preferences will induce highly polarized communication and a loss in utility for any equilibrium. We show that for fat-tailed anecdote distributions the receiver might even prefer to talk to poorly informed senders with aligned preferences rather than a knowledgeable expert whose preferences may differ from her own. We also show that under commitment differences in personal preferences no longer affect communication and the sender will generally report the most representative anecdote closest to the posterior mean for common distributions. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.13461&r= |
| By: | Hao Wu (Hunan University); Rene van den Brink (Vrije Universiteit Amsterdam); Arantza Estevez-Fernandez (Vrije Universiteit Amsterdam) |
| Abstract: | This paper analyzes the allocation of the total toll collected in a highway among its segments. Based on different toll charging rules, we propose the Segments Equal Sharing method, the Exits Equal Sharing method, and the Entrances Equal Sharing method. We provide axioms and characterize these methods used to distribute the toll. Besides, we show how these methods can be obtained by applying the Shapley value to associated coalitional transferable utility games. |
| Keywords: | Highway toll allocation problem, Axiomatic characterization, Shapley value |
| JEL: | R49 C71 |
| Date: | 2022–06–07 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20220036&r= |
| By: | Hao Wu (Hunan University); Rene van den Brink (Vrije Universiteit Amsterdam); Arantza Estevez-Fernandez (Vrije Universiteit Amsterdam) |
| Abstract: | Cooperative games with a permission structure are useful tools for analyzing the impact of hierarchical structures on allocation problems in Economics and Operations Research. In this paper, we propose a generalization of the local disjunctive and the local conjunctive permission approaches called the k-local permission approach. In this approach, every player needs permission from a certain number of its predecessors to cooperate in a coalition. The special case where every player needs permission from at least one of, respectively all, its predecessors coincides with the local disjunctive, respectively local conjunctive, approach in the literature. We de ne and characterize a corresponding k-local permission value. After that, we apply this value to de ne a new class of power measures for directed graphs. We axiomatize these power measures, and apply some of them to two classical networks in the literature. |
| Keywords: | TU-game, Hierarchical structure, Shapley value, Axiomatization, Digraph, Power measure |
| JEL: | C71 |
| Date: | 2022–06–07 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20220037&r= |
| By: | Lambrecht, Marco; Oechssler, Jörg |
| Abstract: | A risky skill game is a game in which skill plays an important role but outcomes are also strongly influenced by random factors. Examples are poker or blackjack but also many economic activities like trading on financial markets. In an online experiment we let subjects choose how often they want to play a risky skill game. We find that women play only half as many rounds in risky skill games if the influence of chance is large. There is no gender difference if the influence of chance is small or if outcomes depend exclusively on chance. |
| Keywords: | gender; risk; competitiveness |
| Date: | 2022–06–10 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0717&r= |
| By: | P. Battiston; M. Menegatti |
| Abstract: | Prevention efforts often involve spillovers, positive or negative, on other individuals, but this is neglected by standard models of risk prevention. We analyze strategic interaction between decision makers whose effort affects each other's risk. We characterize response functions and Nash equilibria, providing proof of existence and analyzing the Pareto efficiency and possible multiplicity of equilibria. We then analyze the optimal effort level from a social point of view, finding conditions under which Nash equilibria are characterized by under- or over-provision of effort, which calls for policy interventions. Finally, we specialize our model to describe the risk of COVID-19 infection. The features of contagion are consistent with the existence of asymmetric equilibria where the high effort exerted by one decision maker pushes another to exert low effort. Moreover, socially optimal mandatory policies, for instance concerning face masks, can cause a decision maker to decrease exerted effort. |
| Keywords: | prevention, interaction, COVID-19, contagion |
| JEL: | D81 C72 I12 |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:par:dipeco:2022-ep02&r= |
| By: | Ritesh Jain and (Institute of Economics, Academia Sinica.); Michele Lombardi (University of Liverpool Management School, Università di Napoli Federico II, and CSEF) |
| Abstract: | Interim Rationalizable Monotonicity, due to Oury and Tercieux (2012), fully characterizes the class of social choice functions that are implementable in interim correlated rationalizable (and Bayes-Nash equilibrium) strategies. |
| Keywords: | temporary contracts, young workers, flexibility, institutional reforms, employment protection legislation. |
| JEL: | C79 D82 |
| Date: | 2022–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:645&r= |
| By: | Srinivas Arigapudi; Omer Edhan; Yuval Heller; Ziv Hellman |
| Abstract: | We study games in which the set of strategies is multi-dimensional, and new agents might learn various strategic dimensions from different mentors. We introduce a new family of dynamics, the recombinator dynamics, which is characterised by a single parameter, the recombination rate r in [0,1]. The case of r = 0 coincides with the standard replicator dynamics. The opposite case of r = 1 corresponds to a setup in which each new agent learns each new strategic dimension from a different mentor, and combines these dimensions into her adopted strategy. We fully characterise stationary states and stable states under these dynamics, and we show that they predict novel behaviour in various applications. |
| Date: | 2022–04 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.00278&r= |
| By: | Soo Hong Chew; Wenqian Wang |
| Abstract: | Two dynamic game forms are said to be behaviorally equivalent if they share the "same" profiles of structurally reduced strategies (Battigalli et al., 2020). In the context of dynamic implementation, behaviorally equivalent game forms are interchangeable under a wide range of solution concepts for the purpose of implementing a social choice function. A gradual mechanism (Chew and Wang, 2022), which designs a procedure of information transmission mediated by a central administrator, enables a formal definition of information flow. We provide a characterization of behavioral equivalence between gradual mechanisms in terms of their informational equivalence -- each agent is designed the "same" information flow. Information flow also helps in defining an intuitive notion of immediacy for gradual mechanisms which is equivalent to their game structures being minimal. Given that the class of gradual mechanisms serves as a revelation principle for dynamic implementation (Li, 2017; Akbarpour and Li, 2020; Mackenzie, 2020; Chew and Wang, 2022), the class of immediate gradual mechanisms provides a refined revelation principle. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.10844&r= |
| By: | Wu, Haoyang |
| Abstract: | In a mechanism, a designer may reveal some information to influence agents' private types in order to obtain more payoffs. In the literature, the information is usually represented as random variables, the value of which are realized by the nature. However, this representation of information may not be proper in some practical cases. In this paper, we propose a type-adjustable mechanism where the information sent by the designer is modeled as a solution of her optimization problem. From the designer's perspective, the probability distributions of agents' private types may be optimally controlled. By constructing a type-adjustable first-price sealed-bid auction, we show that the seller may obtain more expected payoffs than what she could obtain at most in the traditional optimal auction model. Interestingly, to the satisfaction of all, each agent's \emph{ex-ante} expected payoffs may be increased too. In the end, we compare the type-adjustable mechanism with other relevant models. |
| Keywords: | Mechanism design; Optimal auction; Bayesian implementation. |
| JEL: | D71 |
| Date: | 2022–05–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:113150&r= |
| By: | Herings, Jean-Jacques (Tilburg University, Center For Economic Research); Khan, Abhimanyu |
| Keywords: | network; stability; limited foresight; heterogeneity in foresight; coalitional deviations; stochastically stable network |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:tiu:tiucen:03f2ece9-902b-4dba-a16e-0dfa9fc16a9e&r= |
| By: | Jacopo Bizzotto; Toomas Hinnosaar; Adrien Vigier |
| Abstract: | We parameterize commitment in leader-follower games by letting the leader publicly choose her action set from a menu of options. We fully characterize for a large class of settings the set of equilibrium outcomes obtained when varying the degree of commitment that the leader has. We identify conditions under which giving more commitment power to the leader could end up making her worse off. Moreover, with partial commitment, the follower might obtain a larger payoff than the leader even in settings where the latter possesses a first-mover advantage under full commitment. We explore the implications of our analysis for oligopolies. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.05546&r= |
| By: | Arash Abizadeh; Adrian Vetta |
| Abstract: | If a measure of voting power assigns greater voting power to a player because it no longer effectively cooperates with another, then the measure displays the quarrelling paradox and violates the quarrel postulate. We provide formal criteria by which to judge whether a given conception of quarrelling is (a) reasonable and (b) fit to serve as the basis for a reasonable quarrel postulate. To achieve this, we formalize a general framework distinguishing between three degrees of quarrelling (weak, strong, cataclysmic), symmetric vs. asymmetrical quarrels, and reciprocal vs. non-reciprocal quarrels, and which thereby yields twelve conceptions of quarrelling, which encompasses the two conceptions proposed by Felsenthal and Machover and by Laruelle and Valenciano, respectively. We argue that the two existing formulations of the quarrel postulate based on these conceptions are unreasonable. In contrast, we prove that the symmetric, weak conception of quarrelling identified by our framework -- whether reciprocal or not -- is fit to serve as the basis for a reasonable quarrel postulate. Furthermore, the classic Shapley-Shubik index and Penrose-Banzhaf measure both satisfy the quarrel postulate based on a symmetric weak quarrel. |
| Date: | 2022–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2205.08353&r= |
| By: | Tri Vi Dang; Xiaoxi Liu; Florian Morath |
| Abstract: | This paper shows that a transaction tax makes trades in decentralized markets more information sensitive and enlarges the range of information costs for which the equilibrium exhibits private information acquisition and endogenous adverse selection. A transaction tax reduces the probability of trade. The opposite implications hold for a tax on capital gains. The theoretical implications of a transaction tax are tested using a tax policy change in one segment of Singapore’s housing market. Using various proxies for information sensitivity, the triple difference-in-difference analysis shows that a higher transaction tax reduces turnover more strongly when trades are more information sensitive. |
| Keywords: | Bargaining, information acquisition, taxation, transaction tax, capital gains tax, tax incidence, decentralized markets, housing markets, policy experiment, information sensitivity |
| JEL: | C78 D82 D83 G18 H20 |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2022-08&r= |