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on Game Theory |
| By: | Flesch János; Kuipers Jeroen; Mashiah-Yaakovi Ayala; Schoenmakers Gijs; Solan Eilon; Vrieze Koos (METEOR) |
| Abstract: | We prove that every multi-player Borel game with bounded and lower-semi-continuous payoffs admits a subgame-perfect epsilon-equilibrium in pure strategies. This result complements Example 3 in Solan and Vieille (2003), which shows that a subgame-perfect epsilon-equilibrium in pure strategies need not exist when the payoffs are not lower-semi-continuous. In addition, if the range of payoffs is finite, we characterize in the form of a Folk Theorem the set of all plays and payoffs that are induced by subgame-perfect 0-equilibria in pure strategies. |
| Keywords: | mathematical economics; |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2010040&r=gth |
| By: | Peeters Ronald; Saran Rene; Yuksel Ayse Muge (METEOR) |
| Abstract: | We study a spatial model of party formation in which the set of agendas is the unit circle. We characterize the sets of pure-strategy Nash equilibria under the plurality and proportional rules. In both rules, multiple configurations of parties are possible in Nash equilibrium. We refine our predictions using a new notion called “defection-proof” Nash equilibrium. Under the plurality rule, only those Nash equilibria in which either two or three parties exist are defection-proof, whereas multiple parties exist in any defectionproof Nash equilibrium under the proportional rule. These results are mostly consistent with the predictions of Duverger (1954).Keywords: Party Formation; Spatial Model; Plurality Rule; Proportional Rule; Nash Equilibrium; Defection-Proof Nash Equilibrium. |
| Keywords: | microeconomics ; |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2010045&r=gth |
| By: | David Baqaee and Richard Watt (Reserve Bank of New Zealand) |
| Abstract: | Consider an n-person bargaining problem where players bargain over the division of a cake whose size is stochastic. In such a game, the players are not only bargaining over the division of a cake, but they are also sharing risk. This paper presents the Nash bargaining solution to this problem, investigates its properties, and highlights a few special cases. |
| JEL: | C23 D10 R20 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:nzb:nzbdps:2010/06&r=gth |
| By: | Roy, Sunanda; Sabarwal, Tarun |
| Date: | 2010–09–28 |
| URL: | http://d.repec.org/n?u=RePEc:isu:genres:32009&r=gth |
| By: | Gabrielle Demange; Xiaotie Deng |
| Abstract: | This article surveys studies on universally balanced properties of cooperative games defined in a succinct form. In particular, we focus on combinatorial optimization games in which the values to coalitions are defined through linear optimization programs, possibly combinatorial, that is subject to integer constraints. In economic settings, the integer requirement reflects some forms of indivisibility. We are interested in the classes of games that guarantee a non-empty core no matter what are the admissible values assigned to the parameters defining these programs. We call such classes universally balanced. We present characterization and complexity results on the universally balancedness property for some classes of interesting combinatorial optimization games. In particular, we focus on the algorithmic properties for identifying universally balancedness for the games under discussion. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:pse:psecon:2010-28&r=gth |
| By: | Dan Kovenock (Department of Economics, The University of Iowa); Brian Roberson (Department of Economics, Krannert School of Management, Purdue University); Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University) |
| Abstract: | This paper experimentally examines behavior in a two-player game of attack and defense of a weakest-link network of targets, in which the attacker's objective is to successfully attack at least one target and the defender's objective is diametrically opposed. We apply two benchmark contest success functions (CSFs): the auction CSF and the lottery CSF. Consistent with the theoretical prediction, under the auction CSF, attackers utilize a stochastic “guerilla warfare” strategy — in which a single random target is attacked — more than 80% of the time. Under the lottery CSF, attackers utilize the stochastic guerilla warfare strategy almost 45% of the time, contrary to the theoretical prediction of an equal allocation of forces across the targets. |
| Keywords: | Colonel Blotto, conflict resolution, weakest-link, best-shot, multi-dimensional resource allocation, experiments. |
| JEL: | C72 C91 D72 D74 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:10-14&r=gth |
| By: | Rene van den Brink (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam) |
| Abstract: | In this paper we consider the problem of sharing water from a river among a group of agents (countries, cities, firms) located along the river. The benefit of each agent depends on the amount of water consumed by the agent. An allocation of the water among the agents is efficient when it maximizes the total benefits. To sustain an efficient water allocation, the agents can compensate each other by paying monetary transfers. Every water allocation and transfer schedule yields a welfare distribution, where the utility of an agent is equal to its benefit from the water consumption plus its monetary transfer (which can be negative). The problem of finding a fair welfare distribution can be modelled by a cooperative game. For a river with one spring and increasing benefit functions, Ambec and Sprumont (2002) propose the downstream incremental solution as the unique welfare distribution that is core-stable and satisfies the condition that no agent gets a utility payoff above its aspiration level. Ambec and Ehlers (2008) generalized the Ambec and Sprumont river game to river situations with satiable agents, i.e., the benefit function is decreasing beyond some satiation point. In such situations externalities appear, yielding a cooperative game in partition function form. In this paper we consider river situations with satiable agents and with multiple springs. For this type of river systems we propose the class of so-called weighted hierarchical solutions as the class of solutions satisfying several principles to be taken into account for solving water disputes. When every agent has an increasing benefit function (no externalities) then every weighted hierarchical solution is core-stable. In case of satiation points, it appears that every weighted hierarchical solution is independent of the externalities. |
| Keywords: | water allocation; river game; externality; core; hierarchical outcome |
| JEL: | C71 D62 H23 |
| Date: | 2010–09–20 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20100096&r=gth |
| By: | Goette, Lorenz (University of Lausanne); Huffman, David (Swarthmore College); Meier, Stephan (Columbia University); Sutter, Matthias (University of Innsbruck) |
| Abstract: | We investigate how group boundaries, and the economic environment surrounding groups, affect altruistic cooperation and punishment behavior. Our study uses experiments conducted with 525 officers in the Swiss Army, and exploits random assignment to platoons. We find that, without competition between groups, individuals are more prone to cooperate altruistically in a prisoner's dilemma game with in-group as opposed to out-group members. They also use a costly punishment option to selectively harm those who defect, encouraging a norm of cooperation towards the group. Adding competition between groups causes even stronger in-group cooperation, but also a qualitative change in punishment: punishment becomes antisocial, harming cooperative and defecting out-group members alike. These findings support recent evolutionary models and have important organizational implications. |
| Keywords: | group membership, competition, punishment, army, experiment |
| JEL: | C72 C91 C93 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp5189&r=gth |
| By: | Jorge Alcalde-Unzu; Marc Vorsatz |
| Abstract: | In this paper, we suggest new ways of how to measure the similarity of preferences in a group of individuals. For simplicity, we refer to this as the cohesiveness (of preferences). We propose axioms a cohesiveness measure should satisfy and show that these properties fully characterize a family of measures. According to it, the similarities between each pair of objects in a preference profile -calculated as the proportion margin by which one objects wins against the other in a pairwise comparison- are aggregated by a weighted mean. The weight of each pair of objects depends on their importance at the social level |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:fda:fdaddt:2010-23&r=gth |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Stephen Morris (Dept. of Economics, Princeton University); Satoru Takahashi (Dept. of Economics, Princeton University) |
| Abstract: | A universal type space of interdependent expected utility preference types is constructed from higher-order preference hierarchies describing (i) an agent's (unconditional) preferences over a lottery space; (ii) the agent's preference over Anscombe-Aumann acts conditional on the unconditional preferences; and so on. Two types are said to be strategically indistinguishable if they have an equilibrium action in common in any mechanism that they play. We show that two types are strategically indistinguishable if and only if they have the same preference hierarchy. We examine how this result extends to alternative solution concepts and strategic relations between types. |
| Keywords: | Interdependent preferences, Higher-order preference hierarchy, Universal type space, Strategic distinguishability |
| JEL: | C79 D82 D83 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1772&r=gth |
| By: | David Hugh-Jones (Max Planck Institute of Economics, Jena); David Reinstein (Department of Economics at Essex University) |
| Abstract: | When person A makes an offer to person B and B rejects it, then A may "lose face". This loss of face is assumed to occur only if B knows for sure of A's offer. While under some circumstances loss of face can be rationalized by the consequences for future reputation, it may also enter directly into the utility function. Loss of face concerns can lead to fewer offers and inefficiency in markets that involve matching, discrete transactions, and offers/proposals in both directions, such as the marriage market, certain types of labor markets, admissions to colleges and universities, and joint ventures and collaborations. We offer a simple model of this, and show that under some circumstances welfare can be improved by a mechanism that only reveals offers when both parties say "yes". |
| Keywords: | Matching, marriage markets, anonymity, reputation, adverse selection, Bayesian games, emotions. |
| JEL: | D83 |
| Date: | 2010–09–29 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2010-068&r=gth |
| By: | David Baqaee (Reserve Bank of New Zealand) |
| Abstract: | A compelling, but highly tractable, axiomatic foundation for intertemporal decision making is established and discussed. This axiomatic foundation relies on methods employed in cooperative bargaining theory. Four simple axioms imply that the intertemporal objective function is a weighted geometric average of each period's utility function. This is in contrast to standard practice, which takes the objective function to be a weighted arithmetic average. The analysis covers both finite and infinite time. |
| JEL: | C23 D10 R20 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:nzb:nzbdps:2010/08&r=gth |
| By: | José M. Jiménez Gómez (Universidad Politécnica de Cartagena) |
| Abstract: | As Roemer (1986) points out, things become more interesting once we include information. In this paper, following the line started by Jiménez-Gómez and Marco-Gil (2008), we define both a lower and an upper bounds on awards in the framework of the Lorenz-Bifocal Bankruptcy Problem (Gadea et al. (2010)), which is an extended bankruptcy problem enriched with a Commonly Accepted Equity Principles set and the idea of treat everybody as evenly as possible (Dutta and Ray (1989) and Arin (2007), among others). Moreover, we contribute with the definition of the Lorenz Double Boundedness Recursive procedure, which consists on the recursive imposition of both bounds, providing a natural way of justifying the convex combination of bankruptcy rules. Specifically, we retrieve the midpoint of extreme and opposite well known ways of distributing the resource. Finally, we complete our analysis from the strategic viewpoint, obtaining similar results. |
| Keywords: | bankruptcy problems, lower bound, upper bound, duality, recursivity |
| JEL: | C71 D63 D71 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:ivi:wpasad:2010-29&r=gth |
| By: | Leuven, Edwin (CREST (ENSAE)); Oosterbeek, Hessel (University of Amsterdam); van der Klaauw, Bas (VU University Amsterdam) |
| Abstract: | In this paper we investigate how heterogeneous agents choose among tournaments with different prizes. We show that if the number of agents is sufficiently small, multiple equilibria can arise. Depending on how the prize money is split over the tournaments, these may include, for example, a perfect-sorting equilibrium in which high-ability agents compete in the high-prize tournament, while low-ability agents compete for the low prize. However, there are also equilibria in which agents follow a mixed strategy and there can be reverse sorting, i.e. low-ability agents are in the tournament with the high prize, while high-ability agents are in the low-prize tournament. We show that total effort always decreases compared to a single tournament. However, splitting the tournament may increase the effort of low-ability agents. |
| Keywords: | self-selection, tournament, heterogeneous agents, social planner |
| JEL: | D02 |
| Date: | 2010–09 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp5186&r=gth |
| By: | David Hugh-Jones; Ro'i Zultan |
| Abstract: | In experiments, people behave more cooperatively when they are aware of an external threat, while in the field, we observe surprisingly high levels of cooperation and altruism within groups in conflict situations such as civil wars. We provide an explanation for these phenomena. We introduce a model in which different groups vary in their willingness to help each other against external attackers. Attackers infer the cooperativeness of a group from its members' behaviour under attack, and may be deterred by a group which bands together against an initial attack. Then, even self-interested individuals may behave cooperatively when threatened, so as to mimic more cooperative groups. By doing so, they drive away attackers and increase their own future security. We argue that a group's reputation is a public good with a natural weakest-link structure. We test the implications of our model in a laboratory experiment. |
| Keywords: | cooperation, conflict, defence, signaling |
| JEL: | C73 C92 D74 |
| Date: | 2010–09–27 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2010-064&r=gth |