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on Game Theory |
| By: | Victoria Kreps (National Research University Higher School of Economics) |
| Abstract: | We consider finite non-cooperative N person games with fixed numbers mi, i = 1, . . . , N , of pure strategies of player i. We propose the following question: is it possible to extend the vector space of finite non-cooperative m1 ? m2 ? . . . ? mN - games in mixed strategies such that all games of a broader vector space of non- cooperative N person games on the product of unit (mi ? 1)-dimensional simpleces have Nash equilibrium points? We get a necessary and sufficient condition for the negative answer. This condition consists of a relation between the numbers of pure strategies of the players. For two-person games the condition is that the numbers of pure strategies of the both players are equal |
| Keywords: | Finite non-cooperative N person games, vector space, Nash equilibrium point, maximality. |
| JEL: | C72 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:hig:wpaper:150/ec/2016&r=gth |
| By: | Liza Charroin (Univ Lyon, ENS de Lyon, GATE L-SE UMR 5824, F-69342 Lyon, France) |
| Abstract: | In the benchmark model of Bala and Goyal (2000) on network formation, the equilibrium network is asymmetric and unfair as agents have different payoffs. While they are prominent in reality, asymmetric networks do not emerge in the lab mainly because of fairness concerns. We extend this model with a sequential linking decision process to ease coordination and with heterogeneous agents. Heterogeneity is introduced with the presence of a special agent who has either a higher monetary value or a different status. The equilibrium is asymmetric and unfair. Our experimental results show that thanks to sequentiality and fairness concerns, individuals coordinate on fair and efficient networks in homogeneous settings. Heterogeneity impacts the network formation process by increasing the asymmetry of networks but does not decrease the level of fairness nor efficiency |
| Keywords: | Network formation, sequentiality, heterogeneity, fairness, asymmetry |
| JEL: | C72 C92 D85 Z13 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:1629&r=gth |
| By: | Roberto Burguet; Ramon Caminal |
| Abstract: | We propose a new solution concept for TU cooperative games in characteristic function form, the SCOOP, that builds on the Nash Bargaining Solution (NBS ), adding to it a consistency requirement for negotiations inside every coalition. The SCOOP specifies the probability of success and payoffs of each coalition. Players share the surplus of a coalition according to the NBS, with disagreement payoffs that are computed as the expectation of payoffs in other coalitions, using some common probability distribution, which in turn is derived from the prior distribution. The predicted outcome can be probabilistic or deterministic, but only the efficient coalition can succeed with probability one. We discuss necessary and sufficient conditions for an efficient solution. In either case, the SCOOP always exists, is generically unique, easy to compute, and exhibits smooth comparative statics. We also discuss non-cooperative implementation of the SCOOP. |
| Keywords: | cooperative games, coalitional bargaining, endogenous disagree- ment payoffs, consistent beliefs |
| JEL: | C71 C78 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:923&r=gth |
| By: | Philippe Bich (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics) |
| Abstract: | We introduce the new concept of prudent equilibrium to model strategic uncertainty, and prove it exists in large classes of discontinuous games. When the game is better-reply secure, we show that prudent equilibrium refines Nash equilibrium. In contrast with the current literature, we don't use probabilities to model players' strategies and beliefs about other players' strategies. We provide examples (first-price auctions, location game, Nash demand game, etc.) where the prudent equilibrium is the intuitive solution of the game. |
| Keywords: | prudent equilibrium,Nash equilibrium,refinement,strategic uncertainty,better-reply secure |
| Date: | 2016–06–24 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01337293&r=gth |
| By: | Breinbjerg, Jesper (Department of Business and Economics) |
| Abstract: | We examine a non-cooperative queueing game where a finite number of customers seek service at a bottleneck facility which opens at a given point in time. The facility servers one customer at a time on a first-come, first-serve basis and the amount of time required to service each customer is identically and independently distributed according to some general probability distribution. The customers must individually choose when to arrive at the facility, and they prefer to complete service as early as possible, while minimizing the time spent waiting in the queue. These preferences are captured by a general utility function which is decreasing in the waiting time and service completion time of each customer. Applications of such queueing games range from people choosing when to arrive at a grand opening sale to travellers choosing when to line up at the gate when boarding an airplane. We develop a constructive procedure that characterizes an arrival strategy which constitutes a symmetric Nash equilibrium and show that there is at most one symmetric equilibrium. We accompany the equilibrium characterization with numerically computed examples of symmetric equilibria induced by a non-multilinear utility function. |
| Keywords: | Non-cooperative queueing games; strategic arrivals; Nash equilibrium |
| JEL: | C72 D62 R41 |
| Date: | 2016–09–20 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2016_006&r=gth |
| By: | Roman M. Sheremeta (Weatherhead School of Management, Case Western Reserve University and Economic Science Institute, Chapman University) |
| Abstract: | Researchers have proposed various theories to explain overbidding in rent-seeking contents, including mistakes, systematic biases, the utility of winning, and relative payoff maximization. Through an eight-part experiment, we test and find significant support for the existing theories. Also, we discover some new explanations based on cognitive ability and impulsive behavior. Out of all explanations examined, we find that impulsivity is the most important factor explaining overbidding in contests. |
| Keywords: | rent-seeking, contest, competition, impulsive behavior, experiments |
| JEL: | C72 C91 D01 D72 |
| Date: | 2016 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:16-21&r=gth |
| By: | Dieter Balkenborg (University of Exeter); Josef Hofbauer (University of Vienna); Christoph Kuzmics (University of Graz) |
| Abstract: | Fixed points of the (most) refined best reply correspondence, introduced in Balkenborg, Hofbauer, and Kuzmics (2013), in the agent normal form of extensive form games with perfect recall have a remarkable property. They induce fixed points of the same correspondence in the agent normal form of every subgame. Furthermore, in a well-defined sense, fixed points of this correspondence refine even trembling-hand perfect equilibria, while, on the other hand, reasonable equilibria that are not weak perfect Bayesian equilibria would be fixed points of this correspondence. |
| Keywords: | subgame perfection; Nash equilibrium refinements; backward induction; sequential rationality |
| JEL: | C62 C72 C73 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:grz:wpaper:2016-11&r=gth |
| By: | Tanaka, Yasuhito; Satoh, Atsuhiro |
| Abstract: | We examine maximin and minimax strategies for firms in asymmetric duopoly with differentiated goods. We consider two patterns of game; the Cournot game in which strategic variables of the firms are their outputs, and the Bertrand game in which strategic variables of the firms are the prices of their goods. We call two firms Firm A and B, and will show that the maximin strategy and the minimax strategy in the Cournot game, and the maximin strategy and the minimax strategy in the Bertrand game are all equivalent for each firm. However, the maximin strategy (or the minimax strategy) for Firm A and that for Firm B are not necessarily equivalent, and they are not necessarily equivalent to their Nash equilibrium strategies in the Cournot game nor the Bertrand game.. But, in a special case, where the objective function of Firm B is the opposite of the objective function of Firm A, the maximin strategy for Firm A and that for Firm B are equivalent, and they constitute the Nash equilibrium both in the Cournot game and the Bertrand game. This special case corresponds to relative profit maximization by the firms. |
| Keywords: | maximin strategy, minimax strategy, duopoly |
| JEL: | C72 D43 |
| Date: | 2016–09–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:73925&r=gth |
| By: | Schroyen, Fred; Treich, Nicolas |
| Abstract: | The relationship between wealth and power has long been debated. Nevertheless, this relationship has been rarely studied in a strategic game. In this paper, we study wealth effects in a strategic contest game. Two opposing effects arise: wealth reduces the marginal cost of effort but it also reduces the marginal benefit of winning the contest. We consider three types of contests which vary depending on whether rents and efforts are commensurable with wealth. Our theoretical analysis shows that the effects of wealth are strongly "contestdependent". It thus does not support general claims that the rich lobby more or that low economic growth and wealth inequality spur conflicts. |
| Keywords: | Conflict, contest, rent-seeking, wealth, risk aversion, lobbying, power, redistribution. |
| JEL: | C72 D72 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:30893&r=gth |
| By: | Gabrielle Fack (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics); Julien Grenet (PSE - Paris-Jourdan Sciences Economiques - CNRS - Centre National de la Recherche Scientifique - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENS Paris - École normale supérieure - Paris - École des Ponts ParisTech (ENPC), PSE - Paris School of Economics); Yinghua He (TSE - Toulouse School of Economics - Toulouse School of Economics) |
| Abstract: | We propose novel approaches and tests for estimating student preferences with data from school choice mechanisms, e.g., the Gale-Shapley Deferred Acceptance. Without requiring truth-telling to be the unique equilibrium, we show that the matching is (asymptotically) stable, or justified-envy-free, implying that every student is assigned to her favorite school among those she is qualified for ex post. Having validated the methods in simulations, we apply them to data from Paris and reject truth-telling but not stability. Our estimates are then used to compare the sorting and welfare effects of alternative admission criteria prescribing how schools rank students in centralized mechanisms. |
| Keywords: | Gale-Shapley Deferred Acceptance Mechanism,School Choice,Stable Matching,Student Preferences,Admission Criteria,C78,D47,D50,D61,I21 |
| Date: | 2015–10 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01215998&r=gth |
| By: | Martin Van der linden (Department of Economics, Vanderbilt University) |
| Abstract: | This paper shows that the deferred acceptance mechanism (DA) cannot be improved upon in terms of manipulability in the sense of either Pathak and Sönmez (2013) or or Arribillaga and Massó (2015) without compromising with stability.A conflict between manipulability and fairness is also identified. It is shown that miniworst stable mechanisms that make the set of individuals who match with their worst achievable mate minimal are maximally manipulable among the stable mechanisms. Miniworst mechanisms are also more manipulable than DA in the sense of Arribillaga and Massó (2015). A similar conflict between fairness and manipulability is identified in the case of the median stable mechanism (Teo and Sethuraman, 1998). |
| Keywords: | matching, deferred acceptance, manipulability, one-to-one matching. |
| JEL: | C7 D8 |
| Date: | 2016–09–21 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:vuecon-sub-16-00019&r=gth |
| By: | Martin Van der linden (Department of Economics, Vanderbilt University) |
| Abstract: | Many mechanisms used to select a committee of k members out of a candidates endow voters with some veto power over candidates. Impossibility results are provided showing that, in most cases, even limited veto power implies that the mechanism is not strategy-proof. These impossibilities hold on a large set of domains including the domain of additive preferences and even when probabilistic mechanisms are allowed. |
| Keywords: | Mechanism design, Strategy-proofness, Veto, Probabilistic mechanism, Committee selection |
| JEL: | C7 D7 |
| Date: | 2016–09–21 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:vuecon-16-00018&r=gth |
| By: | Goyal, S. |
| Abstract: | Networks influence human behavior and well being, and realizing this, individuals make conscious efforts to shape their own networks. Over the past decade, economists have combined these ideas with concepts from game theory, oligopoly, general equilibrium, and information economics to develop a general framework of analysis. The ensuing research has deepened our understanding of classical questions in economics and opened up entirely new lines of enquiry. |
| Date: | 2016–09–12 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1652&r=gth |
| By: | Aymeric Lardon (Université Côte d'Azur, France; GREDEG CNRS) |
| Abstract: | Cet article est une revue de littérature concernant les jeux de coalitions appliqués aux oligopoles. Le coeur est un concept de solution approprié sur cette classe de jeux pour traiter la question de la stabilité des accords collusifs entre les entreprises. L'objectif de cet article est de proposer une typologie des marchés oligopolistiques afin de mettre en perspective les différentes contributions de l'étude sur le coeur. Tout au long de notre exposé, nous mettrons en évidence les conditions nécessaires ou suffisantes (cadre de concurrence, taille du marché, hétérogénéité des coûts, transfert de technologies, règles de blocage...) pour qu'un accord collusif stable existe. |
| Keywords: | Jeux de coalitions, Oligopoles, Accord collusif, Coeur, Balancement, Convexité |
| JEL: | C71 D43 |
| Date: | 2016–09 |
| URL: | http://d.repec.org/n?u=RePEc:gre:wpaper:2016-28&r=gth |
| By: | Kukushkin, Nikolai S.; Quah, John K.-H.; Shirai, Koji |
| Abstract: | We provide an example of a data set where all the revealed preference relations seem to be consistent with single crossing differences and yet the revealed preference relations cannot be extended to a complete preference obeying that property |
| Keywords: | monotone comparative statics; single crossing differences; interval dominance; supermodular games; lattices |
| JEL: | C6 C7 D7 |
| Date: | 2016–09–16 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:73760&r=gth |