|
on Game Theory |
| By: | Lars P. Metzger |
| Abstract: | This paper studies a contest in which players with unobservable types may form an alliance in a pre-stage of the game to join their forces and compete for a prize. We characterize the pure strategy equilibria of this game of incomplete information. We show that if the formation of an alliance is voluntary, players do not reveal private information in the process of alliance formation in any equilibrium. In this case there exists a pooling equilibrium without alliances with a unique effort choice in the contest and there exist equilibria in which all types prefer to form an alliance. If the formation of an alliance can be enforced by one player with positive probability there exists an equilibrium in which only the low types prefer to form an alliance. |
| Keywords: | Service quality; non-essential benefits; prices; health plan switching; German sickness funds; SOEP |
| JEL: | C72 D72 D74 D82 |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:rwi:repape:0544&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS); Andres Jiménez-Losada (Escuela Superior de Ingenieros - Universidad de Sevilla); Manuel Ordóñez (Escuela Superior de Ingenieros - Universidad de Sevilla) |
| Abstract: | We introduce cooperative TU-games on concept lattices, where a concept is a pair (S,S' ) with S being a subset of players or objects, and S' a subset of attributes. Any such game induces a game on the set of players/objects, which appears to be a TU-game whose collection of feasible coalitions is a lattice closed under intersection, and a game on the set of attributes. We propose a Shapley value for each type of game, axiomatize it, and investigate the geometrical properties of the core (nonemptiness, boundedness, pointedness, extremal rays). |
| Abstract: | Nous introduisons la notion de jeu coopératif sur les treillis de concepts, où un concept est une paire (S,S' ) avec S un sous-ensemble de joueurs et S' un sous-ensemble d'attributs. Un tel jeu induit un jeu sur l'ensemble des joueurs/objets, qui s'avère être un jeu TU dont la collection des coalitions réalisables est un treillis fermé sous l'intersection, et un jeu sur l'ensemble des attributs. Nous proposons une valeur de Shapley pour chaque type de jeu, l'axiomatisons et étudions les propriétés géométriques du cœur (conditions pour être non vide, borné et pointé). |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-01111670&r=gth |
| By: | Shino Takayama (School of Economics, The University of Queensland); Yuki Tamura (School of Economics, The University of Queensland) |
| Abstract: | Since the introduction of better-reply security by Reny (1999), the literature studying the existence of a pure strategy Nash equilibrium (PSNE) in discontinuous games has grown substantially. In this paper, we introduce a weak notion of better-reply security, which is applicable to both quasiconcave and nonquasiconcave games. Our conditions for feeble better-reply security are simple, easy to verify and particularly useful in electoral competition games. We also provide necessary and sufficient conditions for the existence of a PSNE in a canonical electoral competition game. Finally, this paper demonstrates why a PSNE fails to exist when a particular type of discontinuity exists in a model. |
| Keywords: | Noncooperative games, discontinuous payoffs, pure strategy Nash equilibrium, existence of equilibrium, better-reply security, electoral competitions |
| Date: | 2015–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:qld:uq2004:546&r=gth |
| By: | Heidhues, Paul; Rady, Sven; Strack, Philipp |
| Abstract: | We consider a game of strategic experimentation in which players face identical discrete-time bandit problems with a safe and a risky arm. In any period, the risky arm yields either a success or a failure, and the first success reveals the risky arm to dominate the safe one. When payoffs are public information, the ensuing free-rider problem is so severe that equilibrium experimentation ceases at the same threshold belief at which a single agent would stop, even if players can coordinate their actions through mediated communication. When payoffs are private information and the success probability on the risky arm is not too high, however, the socially optimal symmetric experimentation profile can be supported as a perfect Bayesian equilibrium for sufficiently optimistic prior beliefs, even if players can only communicate via binary cheap-talk messages. |
| Keywords: | Bayesian learning; cheap talk; information externality; mediated communication; strategic experimentation; two-armed bandit |
| JEL: | C73 D83 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10634&r=gth |
| By: | De Francesco, Massimo A.; Salvadori, Neri |
| Abstract: | The paper extends the analysis of price competition among capacity constrained sellers beyond duopoly and symmetric oligopoly. The main focus is on the equilibrium payoffs under triopoly. The paper also includes insightful examples highlighting features of equilibrium which can arise in a triopoly but not in a duopoly. Most notably, the supports of the equilibrium strategies need not be connected, nor need be connected the union of the supports; further, an atom may exist for a firm different from the largest one. |
| Keywords: | Bertrand-Edgeworth; Price game; Oligopoly; Triopoly; Mixed strategy equilibrium |
| JEL: | C72 L13 |
| Date: | 2015–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:64638&r=gth |
| By: | Philippe Bich (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics); Rida Laraki (Ecole Polytechnique [Palaiseau] - Ecole Polytechnique, IMJ - Institut de Mathématiques de Jussieu - UPMC - Université Pierre et Marie Curie - Paris 6 - UP7 - Université Paris Diderot - Paris 7 - CNRS) |
| Abstract: | This paper studies the existence of some known equilibrium solution concepts in a large class of economic models with discontinuous payo functions. The issue is well understood for Nash equilibria, thanks to Reny's better-reply security condition [34], and its recent improvements [3, 25, 35, 36]. We propose new approaches, related to Reny's work, and obtain tight conditions for the existence of an approximate equilibrium and of a sharing rule solution in pure and mixed strategies (Simon and Zame [38]). As byproducts, we prove that many auction games with correlated types admit an approximate equilibrium, and that in any general equilibrium model with discontinuous preferences, there is a sharing rule solution. |
| Date: | 2014–10–06 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-01071678&r=gth |
| By: | Ido Polak (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS); Joseph Abdou (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS) |
| Abstract: | This paper introduces a class of games called the positive semidefinite games, for which we show the absence of mixed and nonstrict ESS's. As a result, a strategy is an ESS if and only if it is strict Nash. One famous example in this class of games is Rock{Paper{Scissors. For a smaller class of games called the positive definite games, we prove a similar result forThis paper introduces a class of games called the positive semidefinite games, for which we show the absence of mixed and nonstrict ESS's. As a result, a strategy is an ESS if and only if it is strict Nash. One famous example in this class of games is Rock{Paper{Scissors. For a smaller class of games called the positive definite games, we prove a similar result for NSS's. This result opens the door to a corollary: for doubly symmetric games, the existence of an ESS is assured. This is an interesting result because of the stronger dynamic stability properties of ESS's as compared to NSS's. The coordination games played on the identity matrix are an example of games in this latter class. NSS's. This result opens the door to a corollary: for doubly symmetricgames, the existence of an ESS is assured. This is an interesting result because of the stronger dynamic stability properties of ESS's as compared to NSS's. The coordination games played on the identity matrix are anexample of games in this latter class. |
| Date: | 2014–03–14 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01066397&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics); Antoine Mandel (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics); Emily Tanimura (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS) |
| Abstract: | We consider a model of influence with a set of non-strategic agents and two strategic agents. The non-strategic agents have initial opinions and are linked through a simply connected network. They update their opinions as in the DeGroot model. The two strategic agents have fixed opinions, 1 and 0 respectively, and are characterized by the magnitude of the impact they can exert on non-strategic agents. Each strategic agent forms a link with one non-strategic agent in order to alter the average opinion that eventually emerges in the network. This procedure defines a zero-sum game whose players are the two strategic agents and whose strategy set is the set of non-strategic agents. We focus on the existence and the characterization of equilibria in pure strategy in this setting. Simple examples show that the existence of a pure strategy equilibrium does depend on the structure of the network. The characterization of equilibrium we obtain emphasizes on the one hand the influenceability of target agents and on the other hand their centrality whose natural measure in our context defines a new concept, related to betweenness centrality, that we call intermediacy. We also show that in the case where the two strategic agents have the same impact, symmetric equilibria emerge as natural solutions whereas in the case where the impacts are uneven, the strategic players generally have differentiated equilibrium targets, the high-impacts agent focusing on centrality and the low-impact agent on influenceability. |
| Abstract: | Nous considérons un modèle d'influence avec un ensemble d'agents non-stratégiques et deux agents stratégiques. Les agents non-stratégiques sont liés par un réseau simplement convexe et leurs opinions évoluent comme dans le modèle de DeGroot. Les deux agents stratégiques ont des opinions fixes, respectivement 1 et 0, et sont caractérisés par l'impact qu'ils exercent sur les croyances des agents non-stratégiques. Chaque agent stratégique forme exactement un lien avec un agent non-stratégique en vue d'influencer l'opinion moyenne limite qui se forme dans le réseau. Cette procédure définie un jeu à somme nulle où les ensembles de stratégie des deux joueurs sont l'ensemble des agents non-stratégiques. Nous nous intéressons à l'existence et à la caractérisation des équilibres de Nash en stratégie pure dans ce cadre. Des exemples simples montrent que l'existence d'équilibres en stratégie pure dépend de la structure du réseau. La caractérisation des équilibres que nous obtenons met en avant d'une part l'influençabilité et d'autre part l'influence des agents cibles que nous mesurons à travers un nouveau concept mesurant l'intermédiation effectuée par un agent. |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-01158168&r=gth |
| By: | Jordi Brandts; Ayça Ebru Giritligil; Roberto A. Weber |
| Abstract: | In many areas of social life, individuals receive information about a particular issue of interest from multiple sources. When these sources are connected through a network, then proper aggregation of this information by an individual involves taking into account the structure of this network. The inability to aggregate properly may lead to various types of distortions. In our experiment, four agents all want to find out the value of a particular parameter unknown to all. Agents receive private signals about the parameter and can communicate their estimates of the parameter repeatedly through a network, the structure of which is known by all players. We present results from experiments with three different networks. We find that the information of agents who have more outgoing links in a network gets more weight in the information aggregation of the other agents than under optimal updating. Our results are consistent with the model of “persuasion bias” of DeMarzo et al. (2003). |
| Keywords: | persuasion bias, experiments, bounded rationality |
| JEL: | C92 D03 D83 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:829&r=gth |
| By: | Isa Hafalir; Fisher James |
| Abstract: | Certain aggregate externalities, like those due to knowledge and public goods, do not change very much in response to changes in two individuals’ actions. Thus, individuals rationally regard the level of the externality as fixed in their negotiations with each other. We leverage this observation to develop a general framework for the existence of stable matchings in large and finite one-to-one matching games, and we characterize intuitive restrictions on preferences that are sufficient for existence. |
| URL: | http://d.repec.org/n?u=RePEc:cmu:gsiawp:-1326939098&r=gth |
| By: | Isa Hafalir; Rustamdjan Hakimov; Dorothea Kubler; Morimitsu Kurino |
| Abstract: | We theoretically and experimentally study a college admissions problem in which colleges accept students by ranking students’ efforts in entrance exams. Students’ ability levels affect the cost of their efforts. We solve and compare equilibria of “centralized college admissions” (CCA) where students apply to all colleges and “decentralized college admissions” (DCA) where students only apply to one college. We show that lower ability students prefer DCA whereas higher ability students prefer CCA. Many predictions of the theory are supported by the experiments, yet we find a number of differences that render DCA less attractive than CCA compared to the equilibrium benchmark. |
| URL: | http://d.repec.org/n?u=RePEc:cmu:gsiawp:-566341594&r=gth |
| By: | Pierre Lescanne (LIP - Laboratoire de l'Informatique du Parallélisme - CNRS - INRIA - UCBL - Université Claude Bernard Lyon 1 - PRES Université de Lyon - ENS Lyon - École normale supérieure - Lyon) |
| Abstract: | Escalation is the fact that in a game (for instance an auction), the agents play forever. It is not necessary to consider complex examples to establish its rationality. In particular, the $0,1$-game is an extremely simple infinite game in which escalation arises naturally and rationally. In some sense, it can be considered as the paradigm of escalation. Through an example of economic games, we show the benefit economics can take of coinduction. |
| Date: | 2013–09–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:ensl-00832490&r=gth |
| By: | Ahmet Ozkardas (Turgut Ozal University, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics) |
| Abstract: | We consider a union-firm wage bargaining in which the preferences of the union and the firm are expressed by sequences of discount rates varying in time. The contribution of the paper is twofold. First, we consider a model in which the union must choose between strike and holdout in case of disagreement. We show that there exist inefficient subgame perfect equilibria in the model where the union engages in several periods of strikes prior to reaching a final agreement. Furthermore, we analyze a wage bargaining in which the firm is allowed to engage in lockouts. We consider a game in which only lockouts are feasible, i.e., strikes are not allowed. We prove that under certain assumptions there is a subgame perfect equilibrium for this game and it leads to an immediate agreement which yields the union a wage contract smaller that the statuts quo contract. Under this equilibrium the firm always locks out the union after its own offer is rejected and holds out after rejecting an offer of the union. |
| Abstract: | Nous considérons un modèle de négociation salariale entre un syndicat et une firme, où les préférences du syndicat et de la firme sont exprimées par des taux d'escompte variant dans le temps. Les contributions de cet article sont les suivantes. D'abord, nous considérons un modèle où la firme doit décider si elle fait grève quand il n'y a pas d'accord entre les deux parties de la négociation. Nous montrons qu'il y a des équilibres en sous-jeu parfait inefficaces dans le modèle où le syndicat s'engage dans plusieurs périodes de grèves avant de parvenir à un accord final. En outre, nous analysons un modèle où la firme est autorisée à s'engager dans des « lockouts ». Nous considérons un jeu dans lequel seuls les « lockouts » sont possibles, à savoir, les grèves ne sont pas autorisées. Nous montrons que, sous certaines hypothèses, il y a un équilibre en sous-jeu parfait de ce jeu et il aboutit à un accord immédiat qui donne le syndicat d'un contrat de salaire plus faible que le contrat du statu quo. |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01113240&r=gth |
| By: | Joseph Abdou (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS); Nikolaos Pnevmatikos (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS); Marco Scarsini (Engineering and System Design Pillar - Singapore University of Technology and Design) |
| Abstract: | We introduce the classes of uniform and non interactive games. We study appropriate projection operators over the space of games, in order to propose a novel canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the uniform with zero constant, the non interactive total sum zero and the constant components. Under a natural inner product, we show that the components are orthogonal and we provide explicit expressions for the closet uniform and non interactive games to a given game. We characterize the set of its approximate equilibria in terms of the uniformly mixed and dominant strategies equilibria profiles of its closest uniform and non interactive games respectively. |
| Abstract: | On introduit les classes des jeux uniformes et non interactives. On étudie les opérateurs appropriés de projection afin de proposer une nouvelle décomposition de l'espace des jeux en somme directe des trois sous-espaces orthogonaux relativement à un produit scalaire naturel. Ainsi, chaque jeu arbitraire se décompose en trois composantes, la composante uniforme avec constante zéro, la composante non interactive avec somme totale zéro et la composante constante. On fournit alors les expressions explicites des jeux uniformes et non interactifs qui sont les plus proches à un jeu donné. Aussi, on caractérise l'ensemble des équilibres approximatifs en termes d'équilibre uniformément mixte et d'équilibre en stratégies dominantes des jeux les plus proches uniforme et non interactif. |
| Date: | 2014–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01147442&r=gth |
| By: | Wei Ma (Department of Economics, University of Pretoria) |
| Abstract: | This paper addresses the issue of how a given piece of information should be transmitted from a better-informed doctor to an ill-informed patient. The information to be transmitted is expressed as a probability distribution on a space of the patient’s possible health states. For a formal analysis of the issue we develop a two-person dynamic game, in which the doctor sends a sequence of messages to the patient to inform him of his health state, and the patient, after receiving each message, chooses an action in an attempt to improve upon his current health status. We study some standard properties of the equilibria of this game; in particular, we show that it has a subgame perfect equilibrium. |
| Keywords: | Information transmission, Dynamic game theory, Subgame perfect equilibrium |
| JEL: | D73 D83 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:pre:wpaper:201530&r=gth |
| By: | Kim Lehrer (Département d'Économique, Université de Sherbrooke); Catherine Porter (Department of Accountancy, Economics and Finance, Heriot-Watt University) |
| Abstract: | We play a modified dictator game in Uganda with students, civil servants, and individ- uals from the private sector. The sample includes both Ugandans and expatriates. In the dictator game, participants divide a sum of (real) money between themselves and a local charity. In a "turning a blind eye" treatment, participants are rst given the choice of knowing the identity of the recipient. Finally, participants are asked whether they wish to add their own money to the amount of the endowment they chose to allocate to their selected charity. Contrary to many experimental findings, non-students (civil servants) are not significantly more generous than students. In fact, after controlling for demographic characteristics, their average donation is significantly lower than that of students. Very few individuals donate their own money, despite 30% of participants donating the full endowment. Attitudes to charities do not predict the amount donated in the expected way. Length: 36 pages |
| Keywords: | Dictator game, charitable giving, philanthropy, Uganda |
| JEL: | C72 D63 D64 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:shr:wpaper:15-07&r=gth |
| By: | Madarász, Kristóf |
| Abstract: | People exaggerate the extent to which their information is shared with others. I introduce such information projections into a large class of Bayesian games where people wrongly think that if they can condition their strategy on an event others can as well. I apply the model to a variety of settings. In the context of social investment, people misattribute the uncertainty others face about their preferences into others having antagonistic preferences. Even if all parties prefer mutual investment, none invests, but comes to believe through interacting with others that she is alone preferring mutual investment. In the context of communication, the model predicts credulity: persuasion by an advisor with a known incentive to lie will nevertheless induce uniformly inflated average posteriors. Complexity of an asset, but greater financial education as well, can enhance such credulity. I extend the model to incorporate ignorance projection and re- late the predictions of projection equilibrium to evidence on common-value trade. Here, consistent with the evidence in Samuelson and Bazerman (1985), the model predicts non-altruistic truth-telling by sellers. For buyers it predicts the winner’s curse and provides a better ?t of the data than BNE or cursed equilibrium. Further applications to zero-sum games and auctions are explored. |
| Keywords: | persuasion belief-bubbles; pluralistic ignorance; projection; social investment |
| JEL: | C7 D03 |
| Date: | 2015–05 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10636&r=gth |
| By: | Anita Kopányi-Peuker (Faculty of Economics and Business, University of Amsterdam, the Netherlands); Theo Offerman (Faculty of Economics and Business, University of Amsterdam, the Netherlands); Randolph Sloof (Faculty of Economics and Business, University of Amsterdam, the Netherlands) |
| Abstract: | One acclaimed role of managers is to monitor workers in team production processes and discipline them through the threat of terminating them from the team (Alchian and Demsetz, 1972). We extend a standard weakest link experiment with a manager that can decide to replace some of her team members at a cost. The amount of contractual commitment (‘termination possibilities’) and the precision of the manager’s monitoring information serve as treatment variables. Our results show that the fear of exclusion has a profound effect on team performance even if workers are imperfectly monitored; the most flexible contract induces the highest output while the one with no firing possibilities leads to the lowest production. However, once the fear is eliminated for some workers, because permanent workers cannot be fired after a probation phase, effort levels steadily decrease. |
| Keywords: | team-production; weakest-link game; exclusion; probation; experiment |
| JEL: | C72 C92 M51 M55 |
| Date: | 2015–05–29 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150067&r=gth |