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on Game Theory |
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Issue of 2012‒02‒08
six papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Derks, Jean (Department of Knowledge Engineering); Peters, Hans (Department of Quantitative Economics); Sudhölter, Peter (Department of Business and Economics) |
| Abstract: | We consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the undominated set, and we show that it consists of finitely many polytopes with a core-like structure. One of these polytopes is the L1-center, consisting of all efficient allocations that minimize the sum of the absolute values of the excesses. The excess Pareto optimal set contains the allocations that are Pareto optimal in the set obtained by ordering the sums of the absolute values of the excesses of coalitions and the absolute values of the excesses of their complements. The L1-center is contained in the excess Pareto optimal set, which in turn is contained in the undominated set. For three-person games all these sets coincide. These three sets also coincide with the core for balanced games and with the anticore for antibalanced games. We study properties of these sets and provide characterizations in terms of balanced collections of coalitions. We also propose a single-valued selection from the excess Pareto optimal set, the min-prenucleolus, which is defined as the prenucleolus of the minimum of a game and its dual. |
| Keywords: | Transferable utility game; core; anticore; core extension; min-prenucleolus |
| JEL: | C71 |
| Date: | 2012–01–06 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2012_004&r=gth |
| By: | Khmelnitskaya, Anna B. (Faculty of Applied Mathematics); Sudhölter, Peter (Department of Business and Economics) |
| Abstract: | t is well-known that the prenucleolus on the class of TU games is characterized by singlevaluedness, covariance under strategic equivalence, anonymity, and the reduced game property. We show that the prenucleolus on the class of TU games restricted to the connected coalitions with respect to communication structures may be characterized by the same axioms and a stronger version of independence of non-connected coalitions requiring that the solution does not depend on the worth of any non-connected coalition. Similarly as in the classical case, it turns out that each of the five axioms is logically independent of the remaining axioms and that an infinite universe of potential players is necessary. Moreover, a suitable definition and characterization of a prekernel for games with communication structures is presented. |
| Keywords: | TU game; solution concept; communication and conference structure; nucleolus |
| JEL: | C71 |
| Date: | 2011–12–10 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:sdueko:2011_010&r=gth |
| By: | Andre Barreira da Silva Rocha (Departament of Economics, University of Leicester); Annick Laruelle (a.laruelle@ikerbasque.org); Peio Zuazo (Departamento de Fundamentos del Análisis Económico I UPV/EHU) |
| Abstract: | We generalise and extend the work of Iñarra and Laruelle (2011) by studying two person symmetric evolutionary games with two strategies, a heterogenous population with two possible types of individuals and incomplete information. Comparing such games with their classic homogeneous version vith complete information found in the literature, we show that for the class of anti-coordination games the only evolutionarily stable strategy vanishes. Instead, we find infinite neutrally stable strategies. We also model the evolutionary process using two different replicator dynamics setups, each with a different inheritance rule, and we show that both lead to the same results with respect to stability. |
| Date: | 2012–01–24 |
| URL: | http://d.repec.org/n?u=RePEc:ehu:ikerla:201157&r=gth |
| By: | Timothy N. Cason; Sau-Him Paul Lau; Vai-Lam Mui |
| Abstract: | History-dependent strategies are often used to support cooperation in repeated game models. Using the indefinitely repeated common-pool resource assignment game and a perfect stranger experimental design, this paper reports novel evidence that players who have successfully used an efficiency-enhancing turn-taking strategy will teach other players in subsequent supergames to adopt this strategy. We find that subjects engage in turn taking frequently in both the Low Conflict and the High Conflict treatments. Prior experience with turn taking significantly increases turn taking in both treatments. Moreover, successful turn taking often involves fast learning, and individuals with turn taking experience are more likely to be teachers than inexperienced individuals. The comparative statics results show that teaching in such an environment also responds to incentives, since teaching is empirically more frequent in the Low Conflict treatment with higher benefits and lower costs. |
| Keywords: | Learning, Teaching, Assignment Game, Laboratory Experiment, Repeated Games, Turn Taking, Common-Pool Resources |
| JEL: | C73 C91 |
| Date: | 2011–12 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1267&r=gth |
| By: | Dan Kovenock; Brian Roberson |
| Abstract: | In our original comment, we showed that Hausken's characterization of Nash equilibrium is invalid for much of the parameter space examined and provided necessary conditions for his solution to hold. Most of the comments in his reply are either tangential or irrelevant. However, several of the claims made in the reply reveal continuing misunderstandings and gaps in his understanding. In this rejoinder, we brie y clarify the fundamental issues. |
| Keywords: | Game theory; OR in military; Con ict, Contest, Network, Colonel Blotto game |
| JEL: | C72 D74 H56 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1268&r=gth |
| By: | Battaglini, Marco; Nunnari, Salvatore; Palfrey, Thomas |
| Abstract: | We present a legislative bargaining model of the provision of a durable public good over an infinite horizion. In each period, there is a societal endowment which can either be invested in the public good or consumed. We characterize the optimal public policy, defined by the time path of investment and consumption. In each period, a legislature with presentatives of each of n districts bargain over the current period's endowment for investment in the public good and transfers to each district. We analyze the Markov perfect equilibrium under different voting q-rules where q is the number of yes votes required for passage. We show that the efficiency of the public policy is increasing in q because higher q leads to higher investment in the public good and less pork. We examine the theoretical equilibrium predictions by conducting a laboratory experiment with fiveperson committees that compares three alternative voting rules: unanimity (q=5); majority (q=3); and dictatorship (q=1). -- |
| Keywords: | dynamic political economy,voting,public goods,bargaining,experiments |
| JEL: | D71 D72 C78 C92 H41 H54 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2011205&r=gth |