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on Game Theory |
| By: | Jacques Durieu (University of Saint Etienne, France); Hans Haller (Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg VA, USA); Nicolas Querou (Department of Economics, Queen's University, Belfast, Northern Ireland, UK.); Philippe Solal (University of Saint Etienne, France) |
| Abstract: | We study strategic games where players' preferences are weak orders which need not admit utility representations. First of all, we ex- tend Voorneveld's concept of best-response potential from cardinal to ordi- nal games and derive the analogue of his characterization result: An ordi- nal game is a best-response potential game if and only if it does not have a best-response cycle. Further, Milgrom and Shannon's concept of quasi- supermodularity is extended from cardinal games to ordinal games. We find that under certain compactness and semicontinuity assumptions, the ordinal Nash equilibria of a quasi-supermodular game form a nonempty complete lattice. Finally, we extend several set-valued solution concepts from cardinal to ordinal games in our sense. |
| Keywords: | Ordinal Games, Potential Games, Quasi-Supermodularity, Rationalizable Sets, Sets Closed under Behavior Correspondences |
| JEL: | C72 |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:eth:wpswif:07-74&r=gth |
| By: | Jean-Francois Mertens; Abraham Neyman; Dinah Rosenberg |
| Abstract: | We prove that games with absorbing states with compact action sets have a value. |
| Keywords: | Games; Stochastic Games; Zero-sum; Minimax; Absorbing States; Value |
| JEL: | C73 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp456&r=gth |
| By: | Amil Dasgupta; Jakub Steiner; Colin Stewart |
| Abstract: | We study how the presence of multiple participation opportunities coupled with private learning about payoffs affects the ability of agents to coordinate efficiently in global coordination games. Two players face the option to invest irreversibly in a project in one of many rounds. The project succeeds if some underlying state variable q is positive and both players invest, possibly asynchronously. In each round they receive informative private signals about q, and asymptotically learn the true value of q. Players choose in each period whether to invest or to wait for more precise information about q. We show that with sufficiently many rounds, both players invest with arbitrarily high probability whenever investment is socially efficient. This result stands in sharp contrast to the usual static global game outcome in which players coordinate on the risk-dominant action. We provide a foundation for these results in terms of higher order beliefs. |
| Keywords: | Coordination, global games, efficiency, dynamic games, higher-order beliefs |
| JEL: | C72 C73 |
| Date: | 2007–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-301&r=gth |
| By: | Helena Hye-Young Kim (Department of Economics, Korea University); Frans Spinnewyn (Department of Economic, K.U.Leuven); Luc Lauwers (Department of Economic, K.U.Leuven) |
| Abstract: | We investigate the mechanism that provides the optimal decision rule for two agents making joint decisions. It is shown that, a special rectangular mechanism with two sided screening, elicit correct information when agents?preferences are private information. Such mechanism is presented as a game of incomplete information. It is shown that if types are uniformly distributed, then a three stage sequential game with an exogenously given probability of a terminal break down cannot be improved upon within a restricted class of models. |
| Keywords: | Mechanism Design, Efficiency, Risk Limit |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:iek:wpaper:0710&r=gth |
| By: | Helena Hye-Young Kim (Department of Economics, Korea University); Frand Spinnewyn (Department of Economic, K.U.Leuven) |
| Abstract: | The paper examines the behavior of two agents who need to make a joint decision but they have conflicting preferences about the choice of the outcome. Conventionally such problem is considered as the bargaining problem described as the situation of dividing a pie. But we introduce the model that sheds a different light on the problem in question. The problem is described as the conflict situation modelled as a two-stage game. In the first stage players propose outcomes. The settlement is made if the proposed outcomes are the same. If not, the game moves onto the second stage where they play the concession game called the escalation game. In the escalation game, each player, in turn, has the choice between either to submit by accepting the other’s demand or to escalate by way of insisting his demand to be accepted. Each escalation generates a probability of an inefficient outcome. There are two main findings: (1) it is shown that the player’s decision is determined by his risk limit which measures his intensity towards winning. (2) if the escalation game allocates the demand of the player with the highest risk limit, then players propose the Nash cooperative solution. |
| Keywords: | Bargaining, Risk Limit, Nash Bargaining Solution |
| JEL: | C72 C78 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:iek:wpaper:0709&r=gth |
| By: | Yakov Babichenko |
| Abstract: | We study the problem of reaching Nash equilibria in multi-person games that are repeatedly played, under the assumption of uncoupledness: every player knows only his own payoff function. We consider strategies that can be implemented by ?finite-state automata, and characterize the minimal number of states needed in order to guarantee that a pure Nash equilibrium is reached in every game where such an equilibrium exists. |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp459&r=gth |
| By: | Stephen Morris; Hyun Song Shin |
| Date: | 2007–10–31 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001638&r=gth |
| By: | Luca Lambertini (University of Bologna and The Rimini Centre for Economics Analysis, Italy.); Arsen Palestini (University of Bologna, Italy) |
| Abstract: | A differential oligopoly game with advertising is investigated, where different dynamics occur between two groups of agents, the former playing a competitive Nash game and the latter cooperating as a cartel. Sufficient conditions for stability and a qualitative analysis of the profit ratio and social welfare at equilibrium are provided. A threshold value for the size of the competitive fringe is pointed out by a suitable numerical simulation. |
| Keywords: | Advertising, Differential games, Oligopoly, Collusion |
| JEL: | C73 D43 D92 L13 M37 |
| Date: | 2007–07 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:48-07&r=gth |
| By: | Fabrice Barthélémy (THEMA, Université de Cergy-Pontoise); Mathieu MARTIN (THEMA, Université de Cergy-Pontoise); Vincent MERLIN (CREM, CNRS and Université de Caen, Faculté de sciences économiques et de gestion,) |
| Abstract: | A classical problem in the power index literature is to design a voting mechanism such as the distribution of power of the different players is equal (or closer) to a pre established target. This tradition is especially popular when considering two tiers voting mechanisms: each player votes in his own jurisdiction to designate a delegate for the upper tier; and the question is to assign a certain number of mandates for each delegate according the population of the jurisdiction he or she represents. Unfortunately, there exist several measures of power, which in turn imply different distributions of the mandates for the same pre established target. The purposes of this paper are twofold: first, we calculate the probability that the two most important power indices, the Banzhaf index and the Shapley-Shubik index, lead to the same voting rule when the target is the same. Secondly, we determine which index on average comes closer to the pre established target. |
| Keywords: | Banzhaf, Shapley-Shubik, power indices |
| JEL: | C7 D7 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2007-25&r=gth |
| By: | Alex Dickson (Keele University, Centre for Economic Research and School of Economic and Management Studies); Roger Hartley (Department of Economics, University of Manchester) |
| Abstract: | We show in the context of a bilateral oligopoly where all agents are allowed to behave strategically the unexpected result that when the number of buyers becomes large the outcomes in a strategic market game do not converge to those at the Cournot equilibrium. However, convergence to Cournot outcomes is restored if the game is sequential: sellers move simultaneously as do buyers, but the former always move before the latter. This suggests that the ability to commit to supply decisions is an essential feature of Cournot equilibrium. |
| Keywords: | Cournot competition, strategic market game, strategic foundation. |
| JEL: | C72 D43 D51 L13 |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:kee:kerpuk:2007/14&r=gth |
| By: | Jaromir Kovarik |
| Abstract: | We analyze first-order beliefs in a variation of the Public Good Game. We show that (1) the role that belief elicitation plays in the experiment affects both the contribution behavior and beliefs, and (2) framing influences stated beliefs, as much as contribution behavior. In the second part of the paper, we study the role of heterogeneity in the formation of initial beliefs, and provide an empirical model of the belief up-dating process. Subjects use the past experience, stressing the role of experience that comes from situations similar to the current ones. |
| Keywords: | Beliefs, Public Good, Framing, Experiment, (Belief) Learning |
| JEL: | C91 D83 D84 H40 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:usi:labsit:016&r=gth |
| By: | Elizabeth Potamites; Andrew Schotter (Department of Politics, New York University) |
| Abstract: | A reading of the literature on cognitive hierarchies leaves the impression that a subject's type is predetermined before he comes into the lab so that the distribution of types is exogenous and immutable across games. In this paper we view the choice of a person's cognitive level as endogenous and explain it by focusing on subject's expectations about the cognitive levels endogenously chosen by others. We run a set of experiments using the 2/3rd?s guessing game where subjects receive public advice ordered by a set of advisors. We discover that certain types of public advice, those that are commonly interpreted as meaningful, are capable of shifting the distribution of observed cognitive types indicating that the distribution is endogenous. |
| Keywords: | Beauty Contest, Cognitive Types, Cognitive Hierarchies |
| JEL: | C72 C91 |
| Date: | 2007–04 |
| URL: | http://d.repec.org/n?u=RePEc:cso:wpaper:0015&r=gth |
| By: | Alex Dickson (Keele University, Centre for Economic Research and School of Economic and Management Studies); Roger Hartley (Department of Economics, University of Manchester) |
| Abstract: | We prove existence and uniqueness of non-autarkic equilibria in bilateral oligopoly assuming only that preferences are binormal and satisfy a weakened version of gross substitutes. We permit complete heterogeneity of preferences and our analysis exploits the fact that payoffs depend only on own strategy and two universal aggregates. This allows us to define strategic versions of supply and demand curves such that non-autarkic Nash equilibria are in 1-1 correspondence with intersections of these curves. The same approach can be used to establish comparative statics under the assumptions above. As examples, we focus on adding players and changing endowments. This competitive approach also allows us to conclude that much of conventional Marshallian analysis is robust to strategic manipulation. |
| Keywords: | Strategic Marshallian cross, strategic manipulation, imperfect competition. |
| JEL: | C72 D43 D50 |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:kee:kerpuk:2007/13&r=gth |
| By: | Bezalel Peleg; Ariel D. Procaccia |
| Abstract: | Implementation theory tackles the following problem: given a social choice correspondence, find a decentralized mechanism such that for every constellation of the individuals' preferences, the set of outcomes in equilibrium is exactly the set of socially optimal alternatives (as specified by the correspondence). In this paper we are concerned with implementation by mediated equilibrium; under such an equilibrium, a mediator coordinates the players' strategies in a way that discourages deviation. Our main result is a complete characterization of social choice correspondences which are implementable by mediated strong equilibrium. This characterization, in addition to being strikingly concise, implies that some important social choice correspondences which are not implementable by strong equilibrium are in fact implementable by mediated strong equilibrium. |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp463&r=gth |
| By: | Joana Pais; Agnes Pinter |
| Abstract: | We present an experimental study where we analyze three well-known matching mechanisms. the Boston, the Gale-Shapley, and the Top Trading Cycles mechanisms. in di¤erent informational settings. Our experimental results are consistent with the theory, suggesting that the TTC mechanism outperforms both the Boston and the Gale-Shapley mechanisms in terms of efficiency and it is slightly more successful than the Gale-Shapley mechanism regarding the proportion of truthful preference revelation, whereas manipulation is stronger under the Boston mechanism. In addition, even though agents are much more likely to revert to truth-telling in lack of information about the others. payoffs. ignorance may be beneficial in this context. , the TTC mechanism results less sensitive to the amount of information that participants hold. These results therefore suggest that the use of the TTC mechanism in practice is more desirable than of the others. |
| Keywords: | Laboratory Experiments |
| JEL: | C92 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:usi:labsit:018&r=gth |
| By: | Sung-Hyuk Ko (ETRI); Byoung Heon Jun (Department of Economics, Korea University) |
| Abstract: | We consider an alternating offer model where the size of the total surplus is stochastic. Furthermore, the size changes during the time when the offer is being considered. As a result the responder may obtain more information than the proposer. We analyze how the asymmetry in ability to access good information affects the bargaining power, both in terms of the resulting share and in terms of the delay in agreement. |
| Keywords: | alternating offer bargaining, stochastic surplus, informational disadvantage |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:iek:wpaper:0711&r=gth |