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p. 168-188
Received: 9 June 2010 / Accepted: 30 June 2010 / Published: 2 July 2010
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| Download PDF Full-text (219 KB) Abstract: In this paper we want to shed some light on what we mean by backward induction and forward induction reasoning in dynamic games. To that purpose, we take the concepts of common belief in future rationality (Perea [1]) and extensive form rationalizability (Pearce [2], Battigalli [3], Battigalli and Siniscalchi [4]) as possible representatives for backward induction and forward induction reasoning. We compare both concepts on a conceptual, epistemic and an algorithm level, thereby highlighting some of the crucial differences between backward and forward induction reasoning in dynamic games.
p. 189-220
Received: 9 June 2010 / Accepted: 14 July 2010 / Published: 15 July 2010
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| Download PDF Full-text (361 KB) | Abstract: We study 4 x 4 games for which the best response dynamics contain a cycle. We give examples in which multiple Shapley polygons occur for these kinds of games. We derive conditions under which Shapley polygons exist and conditions for the stability of these polygons. It turns out that there is a very strong connection between the stability of heteroclinic cycles for the replicator equation and Shapley polygons for the best response dynamics. It is also shown that chaotic behaviour can not occur in this kind of game.
p. 221-225
Received: 13 July 2010 / Accepted: 14 July 2010 / Published: 21 July 2010
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| Download PDF Full-text (94 KB) Abstract: Ion Juvina found an error in our manuscript published in Games. [...]
p. 226-241
Received: 4 June 2010; in revised form: 7 July 2010 / Accepted: 16 July 2010 / Published: 22 July 2010
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| Download PDF Full-text (219 KB) Abstract: We study the stability of social and economic networks when players are farsighted. We first provide an algorithm that characterizes the unique pairwise and groupwise farsightedly stable set of networks under the componentwise egalitarian allocation rule. We then show that this set coincides with the unique groupwise myopically stable set of networks but not with the unique pairwise myopically stable set of networks. We conclude that, if groupwise deviations are allowed then whether players are farsighted or myopic does not matter; if players are farsighted then whether players are allowed to deviate in pairs only or in groups does not matter.
p. 242-261
Received: 8 June 2010; in revised form: 7 July 2010 / Accepted: 28 July 2010 / Published: 29 July 2010
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| Download PDF Full-text (3428 KB) Abstract: We propose a model in which agents of a population interacting according to a network of contacts play games of coordination with each other and can also dynamically break and redirect links to neighbors if they are unsatisfied. As a result, there is co-evolution of strategies in the population and of the graph that represents the network of contacts. We apply the model to the class of pure and general coordination games. For pure coordination games, the networks co-evolve towards the polarization of different strategies. In the case of general coordination games our results show that the possibility of refusing neighbors and choosing different partners increases the success rate of the Pareto-dominant equilibrium.
p. 262-285
Received: 29 June 2010; in revised form: 1 August 2010 / Accepted: 3 August 2010 / Published: 10 August 2010
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| Download PDF Full-text (361 KB) Abstract: We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph) can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph) cannot change over time.
p. 286-298
Received: 29 June 2010 / Accepted: 27 August 2010 / Published: 2 September 2010
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| Download PDF Full-text (183 KB) Abstract: A set of coalition structures P is farsightedly stable (i) if all possible deviations from any coalition structure p belonging to P to a coalition structure outside P are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improvingpath from any coalition structure outside the set leading to some coalition structure in the set, and (iii) if there is no proper subset of P satisfying the first two conditions. A non-empty farsightedly stable set always exists. We provide a characterization of unique farsightedly stable sets of coalition structures and we study the relationship between farsighted stability and other concepts such as the largest consistent set and the von Neumann-Morgenstern farsightedly stable set. Finally, we illustrate our results by means of coalition formation games with positive spillovers.
p. 299-316
Received: 27 May 2010; in revised form: 18 August 2010 / Accepted: 23 August 2010 / Published: 13 September 2010
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| Download PDF Full-text (223 KB) 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.
p. 317-337
Received: 15 July 2010; in revised form: 30 August 2010 / Accepted: 9 September 2010 / Published: 17 September 2010
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| Download PDF Full-text (954 KB) Abstract: Human social networks reshape continuously, as individuals forge new contacts while abandoning existing ones. Simultaneously, individuals adapt their behavior, leading to an intricate interplay been network evolution and behavior evolution. Here, we review a framework, called Active Linking, which allows an analytical treatment of such a co-evolutionary dynamics. Using this framework we showed that an increase in the number of ways of responding to adverse interactions leads an overall increase of cooperation, which is here extended to all two-player social dilemmas. In addition, we discuss the role of the selection pressure in these results.
p. 338-356
Received: 18 May 2010; in revised form: 6 August 2010 / Accepted: 14 September 2010 / Published: 21 September 2010
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| Download PDF Full-text (262 KB) Abstract: We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria exist in supermodular games. Finally, we provide an application to strategic network formation where such solution concepts may be useful.
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