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on Game Theory |
| By: | Heinrich Harald Nax |
| Abstract: | This note introduces transferable utility cooperative games with multiple membership, extending the scope of cooperative game theory to economic environments featuring externalities and membership in multiple coalitions. This wider class of games generalises games in characteristic and partition function form. definitions of the core for this class of games are proposed, under which cooperation is facilitated through the cross-cutting of contractual arrangements with multiple membership. |
| Keywords: | Cooperative Game Theory, Core, Externalities, Multiple Membership |
| JEL: | C71 D62 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:394&r=gth |
| By: | Alparslan-Gok, S.Z.; Branzei, R.; Tijs, S.H. (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper big boss interval games are introduced and various characterizations are given. The structure of the core of a big boss interval game is explicitly described and plays an important role relative to interval-type bi-monotonic allocation schemes for such games. Specifically, each element of the interval core of a big boss interval game is extendable to a bi-monotonic allocation scheme. Furthermore, on the class of big boss interval games two interval solution concepts of value type are defined which can be seen as extensions of the compromise value and the AL-value to the interval setting. It turns out that these interval solutions coincide and generate a bi-monotonic allocation scheme for each big boss interval game. |
| Keywords: | Cooperative games;interval data;big boss games;bi-monotonic allocation schemes;the AL-value;the compromise value |
| JEL: | C71 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200847&r=gth |
| By: | Péter Csóka (Department of Economics, Maastricht University); P. Jean-Jacques Herings (Department of Economics, Maastricht University); László Á. Kóczy (Budapest Tech) |
| Abstract: | We provide two new characterizations of exact games. First, a game is exact if and only if it is exactly balanced; and second, a game is exact if and only if it is totally balanced and overbalanced. The condition of exact balancedness is identical to the one of balancedness, except that one of the balancing weights may be negative while for overbalancedness one of the balancing weights is required to be non-positive and no weight is put on the grand coalition. Exact balancedness and overbalancedness are both easy to formulate conditions with a natural game-theoretic interpretation and are shown to be useful in applications. Using exact balancedness we show that exact games are convex for the grand coalition and we provide an alternative proof that the classes of convex and totally exact games coincide. We provide an example of a game that is totally balanced and convex for the grand coalition,but not exact. Finally we relate classes of balanced, totally balanced, convex for the grand coalition, exact, totally exact, and convex games to one another. |
| Keywords: | Totally Balanced Games, Exact Games, Convex Games |
| JEL: | C71 C61 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:pkk:wpaper:0805&r=gth |
| By: | Dario Sacco (Socioeconomic Institute, University of Zurich); Armin Schmutzler (Socioeconomic Institute, University of Zurich) |
| Abstract: | The paper characterizes the mixed-strategy equilibria in all-pay auctions with endogenous prizes that depend positively on own effort and negatively on the effort of competitors. Such auctions arise naturally in the context of investment games, lobbying games, and promotion tournaments. We also provide an experimental analysis of a special case which captures the strategic situation of a two-stage game with investment preceding homogenous Bertrand competition. We obtain overinvestment both relative to the mixed-strategy equilibrium and the social optimum. |
| Keywords: | All-pay auctions, oligopoly, investment, experiment, overbidding |
| JEL: | C92 D44 L13 O31 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:soz:wpaper:0806&r=gth |
| By: | Vyrastekova, J.; Funaki, Y.; Takeuchi, A. (Tilburg University, Center for Economic Research) |
| Abstract: | We isolate strategic and non-strategic motivations of sanctioning in a repeated public goods game. In two experimental treatments, subjects play the public goods game with the possibility to sanction others. In the STANDARD sanctions treatment, each subject learns about the sanctions received in the same round as they were assigned, but in the SECRET sanctions treatment, sanctions are announced only after the experiment is finished, removing in this way all strategic reasons to punish. We find that sanctioning is similar in both treatments, giving support for nonstrategic explanations of sanctions (altruistic punishment). Interestingly, contributions to the public good in both treatments with sanctioning are higher than when the public goods game is played without any sanctioning, irrespective of announcing the sanctions to their receivers during the play of the game, or only after the game is finished. The mere knowledge that sanctions might be assigned increases cooperation: subjects correctly expect that nonstrategic sanctioning takes place against freeriders. |
| Keywords: | altruistic punishment;nonstrategic sanctions;strategic sanctions;public goods;economic experiment. |
| JEL: | C72 C92 D74 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200848&r=gth |
| By: | Gómez-Rúa, María; Vidal-Puga, Juan |
| Abstract: | We study three values for transferable utility games with coalition structure, including the Owen coalitional value and two weighted versions with weights given by the size of the coalitions. We provide three axiomatic characterizations using the properties of Efficiency, Linearity, Independence of Null Coalitions, and Coordination, with two versions of Balanced Contributions inside a Coalition and Weighted Sharing in Unanimity Games, respectively. |
| Keywords: | coalition structure; coalitional value |
| JEL: | C7 |
| Date: | 2008–05–29 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8904&r=gth |
| By: | Pradeep Dubey und Dieter Sondermann |
| Abstract: | We show that if limit orders are required to vary smoothly, then strategic (Nash) equilibria of the double auction mechanism yield competitive (Walras) allocations. It is not necessary to have competitors on any side of any market: smooth trading is a substitute for price wars. In particular, Nash equilibria are Walrasian even in a bilateral monopoly. |
| Keywords: | Limit orders, double auction, Nash equilibria, Walras equilibria, mechanism design |
| JEL: | C72 D41 D44 D61 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse9_2008&r=gth |
| By: | Said, Maher |
| Abstract: | We examine markets in which multiple buyers with single-unit demand are faced with an infinite sequence of auctions that arrive at random times. Moreover, the set and number of buyers are not fixed throughout this sequence; instead, additional buyers may arrive on the market in each period. Buyer valuations are independently distributed, and objects are stochastically equivalent. We solve for the expected payoffs of agents on both sides of the market, and examine the manner in which the option value of future auctions, and hence bidding behavior, varies with the expected competitiveness of the market in future periods, as well as the frequency at which auctions occur. In addition, we consider the case when buyer valuations are persistent in the sense that distributions are chosen according to a Markov process, and provide a generalization of our result to this setting. |
| Keywords: | Sequential auctions; Random arrivals; Endogenous option value; Stochastic equivalence. |
| JEL: | D44 C73 |
| Date: | 2008–05–28 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:8901&r=gth |
| By: | Michel Grabisch (Université Paris I Panthéon-Sorbonne, CERMSEM, 106-112 Bd de l’Hôpital, 75013 Paris, France); Agnieszka Rusinowska (University of Lyon, Lyon, F-69003, France; CNRS, UMR 5824, GATE, Ecully, F-69130, France; ENS LSH, Lyon, F-69007, France ; Centre Leon Berard, Lyon, F-69003, France) |
| Abstract: | In the paper, we introduce and study generalized weighted influence indices of a coalition on a player, where players have an ordered set of possible actions. Each player has an inclination to choose one of the actions. Due to influence of a coalition of other players, a final decision of the player may be different from his original inclination. An influence in such situations is measured by the general weighted influence index. In a particular case, the decision of the player may be closer to the inclination of the influencing coalition than his inclination was. The weighted influence index which captures such a case is called the positive weighted influence index. We also consider the negative weighted influence index, where a final decision of the player goes farther away from the inclination of the influencing coalition. Some special cases of the weighted influence indices, called a possibility influence index and an equidistributed influence index, are also defined. We consider different influence functions and study their properties. A set of followers and a set of a conditional followers of a given coalition are defined, and their properties are analyzed. We define the concepts of success, decisiveness, luck, and failure for the multi-choice model of influence. |
| Keywords: | decisiveness, follower of a coalition, influence function, influence indices, success |
| JEL: | C7 D7 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:0801&r=gth |
| By: | Daron Acemoglu; Munther A. Dahleh; Ilan Lobel; Asuman Ozdaglar |
| Abstract: | We study the perfect Bayesian equilibrium of a model of learning over a general social network. Each individual receives a signal about the underlying state of the world, observes the past actions of a stochastically-generated neighborhood of individuals, and chooses one of two possible actions. The stochastic process generating the neighborhoods defines the network topology (social network). The special case where each individual observes all past actions has been widely studied in the literature. We characterize pure-strategy equilibria for arbitrary stochastic and deterministic social networks and characterize the conditions under which there will be asymptotic learning -- that is, the conditions under which, as the social network becomes large, individuals converge (in probability) to taking the right action. We show that when private beliefs are unbounded (meaning that the implied likelihood ratios are unbounded), there will be asymptotic learning as long as there is some minimal amount of "expansion in observations". Our main theorem shows that when the probability that each individual observes some other individual from the recent past converges to one as the social network becomes large, unbounded private beliefs are sufficient to ensure asymptotic learning. This theorem therefore establishes that, with unbounded private beliefs, there will be asymptotic learning an almost all reasonable social networks. We also show that for most network topologies, when private beliefs are bounded, there will not be asymptotic learning. In addition, in contrast to the special case where all past actions are observed, asymptotic learning is possible even with bounded beliefs in certain stochastic network topologies. |
| JEL: | C72 D83 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:14040&r=gth |
| By: | Andreas Leibbrandt; Raúl López-Pérez |
| Abstract: | We provide a systematic comparison of punishment from unaffected third parties and affected second parties using a within-subject design in ten simple games. We apply the classification analysis by El-Gamal and Grether (1995) and find that a parsimonious model assuming subjects are either envious or selfish best explains the punishment from both third and second parties. Third and second parties punish richer co-players, even if they chose a socially or Pareto-efficient allocation or if they are merely bystanders who made no choice. Despite their unaffected position, we do not find that third parties punish in a more impartial or normative manner. |
| Keywords: | Envy, fairness, inequity aversion, norms, punishment, reciprocity |
| JEL: | C70 C91 D63 D74 Z13 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:zur:iewwpx:373&r=gth |
| By: | Attila Ambrus; Kareen Rozen |
| Date: | 2008–05–31 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000002161&r=gth |
| By: | Stefania Ottone (EconomEtica and University of Eastern Piedmont; EconomEtica and University of Eastern Piedmont); Ferruccio Ponzano (University of Eastern Piedmont; University of Eastern Piedmont); Luca Zarri (Università di Verona; Dipartimento di Scienze economiche (Università di Verona)) |
| Abstract: | Social norms are ubiquitous in human life. Their role is essential in allowing cooperation to prevail, despite the presence of incentives to free ride. As far as norm enforcement devices are concerned, it would be impossible to have widespread social norms if second parties only enforced them. However, both the quantitative relevance and the motivations underlying altruistic punishment on the part of ‘unaffected’ third parties are still largely unexplored. This paper contributes to shed light on the issue, by means of an experimental design consisting of three treatments: a Dictator Game Treatment, a Third-Party Punishment Game Treatment (Fehr and Fischbacher, 2004) and a Metanorm Treatment, that is a variant of the Third-party Punishment Game where the Recipient can punish the third party. We find that third parties are willing to punish dictators (Fehr and Fischbacher, 2004; Ottone, 2008) and, in doing so, they are affected by ‘reference-dependent fairness’, rather than by the ‘egalitarian distribution norm’. By eliciting players’ normative expectations, it turns out that all of them expect a Dictator to transfer something – not half of the endowment. Consequently, the Observers’ levels of punishment are sensitive to their subjective sense of fairness. A positive relation between the level of punishment and the degree of negative subjective unfairness emerges. Subjective unfairness also affects Dictators’ behaviour: their actual transfers and their ideal transfer are not significantly different. Finally, we interestingly find that third parties are also sensitive to the receivers’ (credible) threat to punish them: as the Dictator’s transfer becomes lower and lower than the Observer’s ideal transfer, the Observer’s reaction is – other things being equal – significantly stronger in the Metanorm Treatment than in the Third-Party Punishment Game Treatment. Hence, despite their being to some extent genuinely nonstrategically motivated, also third parties – like second parties – are sensitive to the costs of punishing. |
| Keywords: | Third-Party Punishment; Moral Sentiments; Material Interests; Subjective Unfairness; Social Norms. |
| JEL: | C72 C9 D63 Z13 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:ver:wpaper:48&r=gth |
| By: | Annelies de Ridder (Radboud University Nijmegen); Agnieszka Rusinowska (GATE, University of Lyon, CNRS, ENS-LSH, Centre Léon Bérard, France); Elena Saiz (Radboud University Nijmegen); Eligius K.M. Hendrix (University of Wageningen,) |
| Abstract: | In this paper, we analyze a spatial model of coalition formation with data from Dutch elections and with theoretical results. First, we study different procedures of coalition formation. The model shows that procedure plays an important role in reaching a coalition agreement and that political parties do not necessarily benefit from being a firstmover. Moreover, it is shown that a decrease in a party’s flexibility can be beneficial in coalition negotiations. Furthermore, we find that certain power sharing tactics do not always lead to an agreement that is in a party’s advantage. The main message put forward is that the process of coalition formation plays a more important role than is usually acknowledged in literature and practice. |
| Keywords: | coalition formation, elections, simultaneous procedure, step-by-step procedure |
| JEL: | C7 D72 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:0806&r=gth |