|
on Game Theory |
| By: | Alger, Ingela; Weibull, Jörgen |
| Abstract: | We provide a generalized definition of evolutionary stability of heritable types in arbitrarily large symmetric interactions under random matching that may be assortative. We establish stability results when these types are strategies in games, and when they are preferences or moral values in games under incomplete information. We show that a class of moral preferences, with degree of morality equal to the index of assortativity are evolutionarily stable. In particular, selfishness is evolutionarily unstable when there is positive assortativity in the matching process. We establish that evolutionarily stable strategies are the same as those played in equilibrium by rational but partly morally motivated individuals, individuals with evolutionarily stable preferences. We provide simple and operational criteria for evolutionary stability and apply these to canonical examples. |
| Keywords: | Evolutionary stability, assortativity, morality, homo moralis, public goods, contests, helping, Cournot competition. |
| JEL: | C73 D01 D03 |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:28319&r=gth |
| By: | Ulrich Faigle (Universität zu Köln - Mathematisches Institut); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | The classical Shapley value is the average marginal contribution of a player, taken over all possible ways to form the grand coalition $N$ when one starts from the empty coalition and adds players one by one. In a previous paper, the authors have introduced an allocation scheme for a general coalition formation model where the evolution of the coalition of active players is ruled by a Markov chain and need not finish with the grand coalition. This note provides an axiomatization which is only slightly weaker than the original one but allows a much more transparent proof. Moreover, the logical independence of the axioms is exhibited. |
| Keywords: | Coalitional game; coalition formation process; Shapley value |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:hal:pseose:halshs-00976923&r=gth |
| By: | Georgios Gerasimou (School of Economics and Finance, University of St Andrews) |
| Abstract: | Two logically distinct and permissive extensions of iterative weak dominance are introduced for games with possibly vector-valued payoffs. The first, iterative partial dominance, builds on an easy-to-check condition but may lead to solutions that do not include any (generalized) Nash equilibria. However, the second and intuitively more demanding extension, iterative essential dominance, is shown to be an equilibrium refinement. The latter result includes Moulin's (1979) classic theorem as a special case when all players' payoffs are real-valued. Therefore, essential dominance solvability can be a useful solution concept for making sharper predictions in multicriteria games that feature a plethora of equilibria. |
| Keywords: | Dominance solvability; Multicriteria games; Partial Dominance; Essential Dominance |
| JEL: | C72 D01 |
| URL: | http://d.repec.org/n?u=RePEc:san:wpecon:1406&r=gth |
| By: | Bajoori, Elnaz; Flesch, Janos; Vermeulen, Dries |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:eid:wpaper:37909&r=gth |
| By: | Giménez-Gómez, José-Manuel (Universitat Rovira i Virgili, Departament d'Economia and CREIP); Subiza, Begoña (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica); Peis, Josep (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica) |
| Abstract: | A minimum cost spanning tree (mcst) problem analyzes the way to effciently connect individuals to a source when they are located at different places. Once the effcient tree is obtained, the question on how allocating the total cost among the involved agents defines, in a natural way, a conflicting claims situation. For instance, we may consider the endowment as the total cost of the network, whereas for each individual her claim is the maximum amount she will be allocated, that is, her connection cost to the source. Obviously, we have a conflicting claims problem, so we can apply claims rules in order to obtain an allocation of the total cost. Nevertheless, the allocation obtained by using claims rules might not satisfy some appealing properties in particular, it does not belong to the core of the associated cooperative game). We will define other natural claims problems that appear if we analyze the maximum and minimum amount that an individual should pay in order to support the minimum cost tree. |
| Keywords: | Minimum cost spanning tree problem; Claims problem; Core |
| JEL: | C71 D63 D71 |
| Date: | 2014–07–28 |
| URL: | http://d.repec.org/n?u=RePEc:ris:qmetal:2014_003&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Alexandre Skoda (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne) |
| Abstract: | The paper aims at generalizing the notion of restricted game on a communication graph, introduced by Myerson. We consider communication graphs with weighted edges, and we define arbitrary ways of partitioning any subset of a graph, which we call correspondences. A particularly useful way to partition a graph is obtained by computing the strength of the graph. The strength of a graph is a measure introduced in graph theory to evaluate the resistance of networks under attacks, and it provides a natural partition of the graph (called the Gusfield correspondence) into resistant components. We perform a general study of the inheritance of superadditivity and convexity for the restricted game associated with a given correspondence. Our main result is to give for cycle-free graphs necessary and sufficient conditions for the inheritance of convexity of the restricted game associated with the Gusfield correspondence. |
| Keywords: | Communication networks;Coalition structure;Cooperative game; Strength of a graph |
| Date: | 2012–08–29 |
| URL: | http://d.repec.org/n?u=RePEc:hal:pseose:hal-00830291&r=gth |
| By: | Nadia Mâagli (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, Università Ca' Foscari Venezia - Calle Larga Foscari); Marco Licalzi (Università Ca' Foscari Venezia - Department of Management) |
| Abstract: | Two agents endowed with different individual conceptual spaces are engaged in a dialectic process to reach a common understanding. We model the process as a simple non-cooperative game and demonstrate three results. When the initial disagreement is focused, the bargaining process has a zero-sum structure. When the disagreement is widespread, the zero-sum structure disappears and the unique equilibrium requires a retraction of consensus: two agents who individually agree to associate a region with the same concept end up rebranding it as a different concept. Finally, we document a conversers' dilemma: such equilibrium outcome is Pareto-dominated by a cooperative solution that avoids retraction. |
| Keywords: | Cognitive maps; language differences; semantic bargaining; organisational codes; mental models |
| Date: | 2014–01 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01025079&r=gth |
| By: | Yehuda John Levy (Nuffield College, University of Oxford); Andrew McLennan (School of Economics, The University of Queensland) |
| Abstract: | Levy (2013) presents examples of discounted stochastic games that do not have stationary equilibria. The second named author has pointed out that one of these examples is incorrect. In addition to describing the details of this error, this note presents a new example by the first named author that succeeds in demonstrating that discounted stochastic games with absolutely continuous transitions can fail to have stationary equilibria. |
| Date: | 2014–07–17 |
| URL: | http://d.repec.org/n?u=RePEc:qld:uq2004:527&r=gth |
| By: | Yannai A. Gonczarowski; Moshe Tennenholtz |
| Abstract: | Can noncooperative behaviour of merchants lead to a market allocation that prima facie seems anticompetitive? We introduce a model in which service providers aim at optimizing the number of customers who use their services, while customers aim at choosing service providers with minimal customer load. Each service provider chooses between a variety of levels of service, and as long as it does not lose customers, aims at minimizing its level of service; the minimum level of service required to satisfy a customer varies across customers. We consider a two-stage competition, in the first stage of which the service providers select their levels of service, and in the second stage --- customers choose between the service providers. (We show via a novel construction that for any choice of strategies for the service providers, a unique distribution of the customers' mass between them emerges from all Nash equilibria among the customers, showing the incentives of service providers in the two-stage game to be well defined.) In the two-stage game, we show that the competition among the service providers possesses a unique Nash equilibrium, which is moreover super strong; we also show that all sequential better-response dynamics of service providers reach this equilibrium, with best-response dynamics doing so surprisingly fast. If service providers choose their levels of service according to this equilibrium, then the unique Nash equilibrium among customers in the second phase is essentially an allocation (i.e. split) of the market between the service providers, based on the customers' minimum acceptable quality of service; moreover, each service provider's chosen level of service is the lowest acceptable by the entirety of the market share allocated to it. Our results show that this seemingly-cooperative allocation of the market arises as the unique and highly-robust outcome of noncooperative (i.e. free from any form of collusion), even myopic, service-provider behaviour. The results of this paper are applicable to a variety of scenarios, such as the competition among ISPs, and shed a surprising light on aspects of location theory, such as the formation and structure of a city's central business district. |
| Date: | 2014–03 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp663&r=gth |
| By: | Carvalho, José-Raimundo; Magnac, Thierry; Xiong, Qizhou |
| Abstract: | We evaluate a simple allocation mechanism of students to majors at college entry that was commonly used in universities in Brazil in the 1990s and 2000s. Students first chose a single major and then took exams that select them in or out of the chosen major. The literature analyzing student placement, points out that this decentralized mechanism is not stable and is not strategy-proof. This means that some pairs of major & students can be made better off and that students tend to disguise their preferences using such a mechanism. We build up a model of performance and school choices in which expectations are carefully specified and we estimate it using cross-section data reporting choices between two medical schools and grade performances at the entry exams. Given those estimates, we evaluate changes in selection and students'expected utilities when other mechanisms are implemented. Results highlight the importance of strategic motives and redistributive effects of changes of the allocation mechanisms. |
| Keywords: | Education, two-sided matching, school allocation mechanism, policy evaluation |
| JEL: | I21 |
| Date: | 2014–06 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:28351&r=gth |
| By: | Daron Acemoglu; Matthew O. Jackson |
| Abstract: | We examine the interplay between social norms and the enforcement of laws. Agents choose a behavior (e.g., tax evasion, production of low-quality products, corruption, substance abuse, etc.) and then are randomly matched with another agent. An agent's payoff decreases with the mismatch between her behavior and her partner's, as well as average behavior in society. A law is an upper bound (cap) on behavior and a law-breaker, when detected, pays a fine and has her behavior forced down to the level of the law. Law-breaking depends on social norms because detection relies, at least in part, on private cooperation and whistle-blowing. Law-abiding agents have an incentive to whistle-blow because this reduces the mismatch with their partner's behavior as well as the overall negative externality. When laws are in conflict with norms so that many agents are breaking the law, each agent anticipates little whistle-blowing and is more likely to also break the law. Tighter laws (banning more behaviors) have counteracting effects, reducing behavior among law-abiding individuals but inducing more law-breaking. Greater fines for law breaking and better public enforcement reduce the number of law-breakers and behavior among law-abiding agents, but increase levels of law breaking among law-breakers (who effectively choose their behavior targeting other high-behavior law-breakers). Within a dynamic version of the model, we show that laws that are in strong conflict with prevailing social norms may backfire, while gradual tightening of laws can be more effective by changing social norms. |
| JEL: | C72 C73 P16 Z1 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:20369&r=gth |
| By: | Lester, Benjamin R. (Federal Reserve Bank of Philadelphia); Visschers, Ludo (University of Edinburgh); Wolthoff, Ronald P. (University of Toronto) |
| Abstract: | In a market in which sellers compete by posting mechanisms, we study how the properties of the meeting technology affect the mechanism that sellers select. In general, sellers have incentive to use mechanisms that are socially efficient. In our environment, sellers achieve this by posting an auction with a reserve price equal to their own valuation, along with a transfer that is paid by (or to) all buyers with whom the seller meets. However, we define a novel condition on meeting technologies, which we call "invariance," and show that the transfer is equal to zero if and only if the meeting technology satisfies this condition. |
| Keywords: | search frictions, matching function, meeting technology, competing mechanisms |
| JEL: | C78 D44 D83 |
| Date: | 2014–07 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp8357&r=gth |