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on Game Theory |
| By: | Somdeb Lahiri (Institute for Financial Management & Research) |
| Abstract: | In this paper we show that a feasible price allocation pair is a market equilibrium of a discrete market game if and only if it solves a linear programming problem. We use this result to obtain computable necessary and sufficient conditions for the existence of market equilibrium. We assume that the production functions of the profit maximizing agents are discrete concave. |
| Keywords: | discrete concave, existence, market equilibrium, linear programming |
| JEL: | C7 D8 |
| Date: | 2005–12–20 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpga:0512005&r=gth |
| By: | Herings,P. Jean-Jacques; Laan,Gerard,van der; Talman,Dolf (METEOR) |
| Abstract: | In this paper we study cooperative games with limited cooperation possibilities, representedby an undirected cycle-free communication graph. Players in the game can cooperate if andonly if they are connected in the graph, i.e. they can communicate with one another. Weintroduce a new single-valued solution concept, the component fairness solution. Our solution is characterized by component efficiency and component fairness. The interpretationof component fairness is that deleting a link between two players yields for both resultingcomponents the same average change in payoff, where the average is taken over the players in the component. Component fairness replaces the axiom of fairness characterizing the Myerson value, where the players whose link is deleted face the same loss in payoff. Thecomponent fairness solution is always in the core of the restricted game in case the gameis superadditive and can be easily computed as the average of n specific marginal vectors,where n is the number of players. We also show that the component fairness solution canbe generated by a specific distribution of the Harsanyi-dividends. |
| Keywords: | operations research and management science; |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2005056&r=gth |
| By: | Josef Hofbauer; Jörg Oechssler; Frank Riedel |
| Abstract: | In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous—time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible boundedly rational learning process in games. In the current paper we study this Brown—von Neumann—Nash dynamics for the case of continuous strategy spaces. We show that for continuous payoff functions, the set of rest points of the dynamics coincides with the set of Nash equilibria of the underlying game. We also study the asymptotic stability properties of rest points. While strict Nash equilibria may be unstable, we identify suffcient conditions for local and global asymptotic stability which use concepts developed in evolutionary game theory. |
| Keywords: | learning in games, evolutionary stability, BNN |
| JEL: | C70 C72 |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse38_2005&r=gth |
| By: | Pradeep Dubey; John Geanakoplos (Cowles Foundation, Yale University) |
| Abstract: | We introduce grading into games of status. Each player chooses effort, producing a stochastic output or score. Utilities depend on the ranking of all the scores. By clustering scores into grades, the ranking is coarsened, and the incentives to work are changed. We first apply games of status to grading exams. Our main conclusion is that if students care primarily about their status (relative rank) in class, they are often best motivated to work not by revealing their exact numerical exam scores (100,99,...,1), but instead by clumping them into coarse categories (A,B,C). When student abilities are disparate, the optimal grading scheme is always coarse. Furthermore, it awards fewer A's than there are alpha-quality students, creating small elites. When students are homogeneous, we characterize optimal grading schemes in terms of the stochastic dominance between student performances (when they shirk or work) on subintervals of scores, showing again why coarse grading may be advantageous. In both the disparate case and the homogeneous case, we prove that absolute grading is better than grading on a curve, provided student scores are independent. We next bring games of money and status to bear on the optimal wage schedule: workers can be motivated not merely by the purchasing power of wages, but also by the status higher wages confer. How should the employer combine both incentive devices to generate an optimal pay schedule? When workers' abilities are disparate, the optimal wage schedule creates different grades than we found with status incentives alone. The very top type should be motivated solely by money, with enormous salaries going to a tiny elite. Furthermore, if the population of workers diminishes as we go up the ability ladder and their disutility for work does not fall as fast, then the optimal wage schedule exhibits increasing wage differentials, despite the linearity in production. When workers are homogeneous, the same status grades are optimal as we found with status incentives alone. A bonus is paid only to scores in the top status grade. |
| Keywords: | Status, Grading, Incentives, Education, Exams, Wages |
| JEL: | C70 I20 I30 |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1544&r=gth |
| By: | Paulo Klinger Monteiro (FGV-EPGE); Frank H. Page Jr (Department of finance, University of Alabama) |
| Abstract: | We introduce a condition, uniform payoff security, for games with separable metric strategy spaces and payoffs bounded and measurable in players' strategies. We show that if any such metric game G is uniformly payoff secure, then its mixed extension G is payoff secure. We also establish that if a uniformly payoff secure metric game G has compact strategy spaces, and if its mixed extension G has reciprocally upper semicontinuous payoffs, then G has a Nash equilibrium in mixed strategies. We provide several economic examples of metric games satisfying uniform payoff security. |
| Keywords: | Uniform payoff security, Nash equilibrium, discontinuous games, mixed extension. |
| JEL: | C72 |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:mse:wpsorb:b05086&r=gth |
| By: | Lingxin Hao; V. Joseph Hotz; Ginger Z. Jin |
| Abstract: | This paper examines reputation formation in intra-familial interactions. We consider parental reputation in a repeated two-stage game in which adolescents decide whether to give a teen birth or drop out of high school, and given adolescent decisions, the parent decides whether to house and support his children beyond age 18. Drawing on the work of Milgrom and Roberts (1982) and Kreps and Wilson (1982), we show that the parent has, under certain conditions, the incentive to penalize older children for their teenage risky behaviors in order to dissuade the younger children from the same risky behaviors. The model generates two empirical implications: the likelihood of teen risky behaviors and parental transfers to a child who engaged in teen risky behaviors will decrease with the number of remaining children at risk. We test these two implications, using data from the National Longitudinal Survey of Youth, 1979 Cohort (NLSY79). Exploiting the availability of repeated observations on individual respondents and of observations on multiple siblings, we find evidence in favor of both predictions. |
| JEL: | J1 |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:11872&r=gth |
| By: | Sven Fischer |
| Abstract: | Assuming inequality averse subjects as modeled by Fehr and Schmidt (1999) or in the ERC model by Bolton and Ockenfels (2000) in ultimatum games with asymmetric conflict payoffs allows to make predictions especially concerning responder acceptance thresholds. These predictions are tested in a laboratory experiment eliciting proposer offers and respondent's acceptance thresholds using the strategy vector method. By and large both models make good predictions. However, they are unable to convincingly explain the observed selfishness on behalf of responders in ultimatum games favoring them in conflict. Overall, observed behavior gives rise to a context dependent interpretation of inequality aversion and to Knez and Camerer's 1995 observation that subjects form 'egocentric assessments of fairness'. |
| Date: | 2005–10 |
| URL: | http://d.repec.org/n?u=RePEc:esi:discus:2005-36&r=gth |
| By: | Sven Fischer; Luis G. Gonzalez; Werner Güth |
| Abstract: | A two-persons bargaining problem often consists of initially incompatible demands that can be unilaterally reduced by sequential concessions. In a 2 x 2 x 2 - factorial design we distinguish between reliable and unreliable concessions, between a static and dynamic settings and between symmetric and asymmetric initial demands. Whereas reliable concessions change the threat point, unreliable concessions do not. In the dynamic setting each player's concession can be conditional on the previous history of play; in the static setting a player's concessions for all bargaining trials are determined at the beginning of the game. In all situations conflict is triggered if neither gives in, or if a maximum number of trials is reached without a feasible agreement. Although our results indicate that conflict is more likely if concessions are reliable, the overall effciency of both institutions is similar. |
| Keywords: | concession bargaining, behavioral economics |
| Date: | 2005–12 |
| URL: | http://d.repec.org/n?u=RePEc:esi:discus:2005-41&r=gth |
| By: | Peters, Michael |
| Abstract: | The paper proves existence of equilibrium in a fairly general version of the pre-marital investment game. The game has discontinuous payoffs, so the method of Reny (1999) is used. Three assumptions are imposed on the matching process that occurs after investments are realized. It must be assortative, it must resolve ties efficiently, and it must not allow externalities. |
| JEL: | C78 |
| Date: | 2005–12–16 |
| URL: | http://d.repec.org/n?u=RePEc:ubc:pmicro:peters-05-12-16-12-42-35&r=gth |
| By: | Werner Güth; M. Vittoria Levati; Axel Ockenfels; Torsten Weiland |
| Abstract: | We study an ultimatum experiment in which the responder does not know the offer when accepting or rejecting. Unconditional veto power leads to acceptances, although proposers are significantly greedier than in standard ultimatum games, and this is anticipated by responders. |
| Keywords: | Ultimatum, Dictator, Fairness, Veto power |
| JEL: | C92 C72 |
| Date: | 2005–11 |
| URL: | http://d.repec.org/n?u=RePEc:esi:discus:2005-39&r=gth |