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on Game Theory |
| By: | Herve Moulin; Indrajit Ray; Sonali Sen Gupta |
| Abstract: | We consider the well-analyzed abatement game (Barrett 1994) and prove that correlation among the players (nations) can strictly improve upon the Nash equilibrium payoffs. As these games are potential games, correlated equilibrium — CE — (Aumann 1974, 1987) cannot improve upon Nash; however we prove that coarse correlated equilibria — CCE — (Moulin and Vial 1978) may do so. We compute the largest feasible total utility and hence the efficiency gain in any CCE in those games: it is achieved by a lottery over only two pure strategy profiles. |
| Keywords: | Abatement game, Coarse correlated equilibrium, Efficiency gain |
| JEL: | C72 Q52 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:lan:wpaper:68684722&r=gth |
| By: | Nakajima, Tetsuya |
| Abstract: | This note examines how the second chance, when provided to a disadvantaged player, can resolve the prisoner’s dilemma. |
| Keywords: | Prisoner’s dilemma, Noncooperative game, Second chance |
| JEL: | C70 C72 C73 |
| Date: | 2014–10–31 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:59937&r=gth |
| By: | Nizar Allouch (Queen Mary University of London); Myrna Wooders (Vanderbilt University) |
| Abstract: | We provide a new proof of the non-emptiness of approximate cores of games with many players of a finite number of types. Earlier papers in the literature proceed by showing that, for games with many players, equal-treatment cores of their "balanced cover games", which are non-empty, can be approximated by equal-treatment ε-cores of the games themselves. Our proof is novel in that we rely on a fixed point theorem. |
| Keywords: | NTU games, Core, Approximate cores, Small group effectiveness, Coalition formation, Payoff dependent balancedness |
| JEL: | C71 C78 D71 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp726&r=gth |
| By: | Mimra, Wanda; Wambach, Achim |
| Abstract: | Riley (1979)'s reactive equilibrium concept addresses problems of equilibrium existence in competitive markets with adverse selection. The game-theoretic interpretation of the reactive equilibrium concept in Engers and Fernandez (1987) yields the Rothschild-Stiglitz (1976)/Riley (1979) allocation as an equilibrium allocation, however multiplicity of equilibrium emerges. In this note we imbed the reactive equilibrium's logic in a dynamic market context with active consumers. We show that the Riley/Rothschild-Stiglitz contracts constitute the unique equilibrium allocation in any pure strategy subgame perfect Nash equilibrium. |
| Keywords: | asymmetric information,competitive insurance market,contract addition,reactive equilibrium |
| JEL: | C72 D82 G22 L10 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:cfswop:483&r=gth |
| By: | Gerhard Sorger; Tapan Mitra |
| Abstract: | We consider a discrete-time dynamic game in which a nite number of players extract a non-renewable resource and derive consumption solely from the extracted amount (cake-eating game). Markov-perfect Nash equilibria can be constructed in this game not only if the players have time-preference factors that are smaller than 1, but also if these factors are equal to or even larger than 1. We demonstrate this result both for the case of identical players and for the case of heterogeneous players. In addition we study the in uence of the model parameters on the equilibrium. |
| JEL: | C73 Q30 |
| Date: | 2014–10 |
| URL: | http://d.repec.org/n?u=RePEc:vie:viennp:1408&r=gth |
| By: | Stéphane Gonzalez (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); 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: | We consider in this paper solutions for TU-games where it is not assumed that the grand coalition is necessarily the final state of cooperation. Partitions of the grand coalition, or balanced collections together with a system of balancing weights interpreted as a time allocation vector are considered as possible states of cooperation. The former case corresponds to the c-core, while the latter corresponds to the aspiration core or d-core, where in both case, the best configuration (called a maximising collection) is sought. We study maximising collections and characterize them with autonomous coalitions, that is, coalitions for which any solution of the d-core yields a payment for that coalition equal to its worht. In particular we show that the collection of autonomous coalitions is balanced, and that one cannot have at the same time a single possible payment (core element) and a single possible configuration. We also introduce the notion of inescapable coalitions, that is, those present in every maximising collection. We characterize the class of games for which the sets of autonomous coalitions, vital coalitions (in the sense of Shellshear and Sudhölter), and inescapable coalitions coincide, and prove that the set of games having a unique maximising coalition is dense in the set of games. |
| Keywords: | Cooperative game; core; balancedness; c-core; aspiration core; coalition formation; autonomous coalitions |
| Date: | 2014–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-01021328&r=gth |
| By: | Sylvain Béal (CRESE, Université de Franche-Comté); Eric Rémila (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne); Philippe Solal (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne) |
| Abstract: | In this article, we study cooperative games with limited cooperation possibilities, represented by a tree on the set of agents. Agents in the game can cooperate if they are connected in the tree. We first derive direct-sum decompositions of the space of TU-games on a fixed tree, and two new basis for these spaces of TU-games. We then focus our attention on the Average (rooted)-Tree solution (see Herings, P., van der Laan, G., Talman, D., 2008. The Average Tree Solution for Cycle-free Games. Games and Economic Behavior 62, 77-92). We provide a basis for its kernel and a new axiomatic characterization by using the classical axiom for inessential games, and two new axioms of invariance, namely Invariance with respect to irrelevant coalitions and Weighted addition invariance on bi-partitions. |
| Keywords: | Average Tree solution, Direct-sum decomposition, Kernel, Weighted addition invariance on bi-partitions, Invariance to irrelevant coalitions. |
| JEL: | C71 |
| Date: | 2014–11 |
| URL: | http://d.repec.org/n?u=RePEc:crb:wpaper:2014-04&r=gth |
| By: | Manuel Förster (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, CORE - Center of Operation Research and Econometrics [Louvain] - Université Catholique de Louvain (UCL) - Belgique); Ana Mauleon (CORE - Center of Operation Research and Econometrics [Louvain] - Université Catholique de Louvain (UCL) - Belgique, CEREC - Université Saint-Louis - Bruxelles); Vincent Vannetelbosch (CORE - Center of Operation Research and Econometrics [Louvain] - Université Catholique de Louvain (UCL) - Belgique, CEREC - Université Saint-Louis - Bruxelles) |
| Abstract: | We investigate the role of manipulation in a model of opinion formation where agents have opinions about some common question of interest. Agents repeatedly communicate with their neighbors in the social network, can exert some effort to manipulate the trust of others, and update their opinions taking weighted averages of neighbors' opinions. The incentives to manipulate are given by the agents' preferences. We show that manipulation can modify the trust structure and lead to a connected society, and thus, make the society reaching a consensus. Manipulation fosters opinion leadership, but the manipulated agent may even gain influence on the long-run opinions. In sufficiently homophilic societies, manipulation accelerates (slows down) convergence if it decreases (increases) homophily. Finally, we investigate the tension between information aggregation and spread of misinformation. We find that if the ability of the manipulating agent is weak and the agents underselling (overselling) their information gain (lose) overall influence, then manipulation reduces misinformation and agents converge jointly to more accurate opinions about some underlying true state. |
| Keywords: | Social networks; trust; manipulation; opinion leadership; consensus; wisdom of crowds |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00881145&r=gth |
| By: | Ahmet Ozkardas (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne); Agnieszka Rusinowska (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne) |
| Abstract: | We provide an equilibrium analysis of a wage bargaining model between a union and a firm in which the union must choose between strike and holdout in case of a disagreement. While in the literature it is assumed that the parties of wage bargaining have constant discount factors, in our model preferences of the union and the firm are expressed by sequences of discount rates varying in time. First, we describe necessary conditions under arbitrary sequences of discount rates for the supremum of the union's payoffs and the infimum of the firm's payoffs under subgame perfect equilibrium in all periods when the given party makes an offer. Then, we determine the equilibrium payoffs for particular cases of sequences of discount rates varying in time. Besides deriving the exact bounds of equilibrium payoffs, we also characterize the equilibrium strategy profiles that support these extreme payoffs. |
| Keywords: | Union; firm bargaining; varying discount rates; subgame perfect equilibrium; equilibrium payoffs |
| Date: | 2014–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-00971403&r=gth |
| By: | Ezra Einy (BGU); Ori Haimanko (BGU); Ram Orzach (Oakland University, USA); Aner Sela (BGU) |
| Abstract: | We study two-player common-value all-pay auctions (contests) with asymmetric information under the assumption that one of the players has an information advantage over his opponent and both players are budget-constrained. We generalize the results for all-pay auctions with complete information, and show that in all-pay auctions with asymmetric information, sufficiently high (but still binding) bid caps do not change the players' expected total effort compared to the benchmark auction without any bid cap. Furthermore, we show that there are bid caps that increase the players' expected total effort compared to the benchmark. Finally, we demonstrate that there are bid caps which may have an unanticipated effect on the players' expected payoffs - one player's information advantage may turn into a disadvantage as far as his equilibrium payoff is concerned. |
| Keywords: | Common-value all-pay auctions, asymmetric information, information advantage, bid caps. |
| JEL: | C72 D44 D82 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:bgu:wpaper:1402&r=gth |
| By: | Georg Nöldeke; Larry Samuelson (University of Basel) |
| Abstract: | We study markets in which agents first make investments and are then matched into potentially productive partnerships. Equilibrium investments and the equilibrium matching will be efficient if agents can simultaneously negotiate investments and matches, but we focus on markets in which agents must first sink their investments before matching. Additional equilibria may arise in this sunk-investment setting, even though our matching market is competitive. These equilibria exhibit inefficiencies that we can interpret as coordination failures. All allocations satisfying a constrained efficiency property are equilibria, and the converse holds if preferences satisfy a separability condition. We identify sufficient conditions (most notably, quasiconcave utilities) for the investments of matched agents to satisfy an exchange efficiency property as well as sufficient conditions (most notably, a single crossing property) for agents to be matched positive assortatively, with these conditions then forming the core of sufficient conditions for the efficiency of equilibrium allocations. |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:bsl:wpaper:2014/07&r=gth |
| By: | Kodritsch, Sebastian |
| Abstract: | This paper analyzes dynamically inconsistent time preferences in Rubinstein's (1982) seminal model of bargaining. When sophisticated bargainers have time preferences that exhibit a form of present bias - satisfied by the hyperbolic and quasi-hyperbolic time preferences increasingly common in the economics literature - equilibrium is unique and lacks delay. However, when one bargainer is more patient about a single period's delay from the present than one that occurs in the near future, the game permits a novel form of equilibrium multiplicity and delay. Time preferences with this property have most recently been empirically documented; they can also arise when parties who weight probabilities non-linearly bargain under the shadow of exogenous breakdown risk, as well as in settings of intergenerational bargaining with imperfect altruism. The paper's main contributions are (i) a complete characterization of the set of equilibrium outcomes and payoffs for separable time preferences, and (ii) present bias as a readily interpretable sufficient condition for uniqueness at the level of individual preferences. |
| Keywords: | bargaining,time preference,dynamic inconsistency,delay |
| JEL: | C78 D03 D74 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2014205&r=gth |
| By: | Matthias Weber (CREED, University of Amsterdam) |
| Abstract: | There are many situations in which different groups make collective decisions by committee voting, where each group is represented by a single person. Theoretical concepts suggest how the voting systems in such committees should be designed, but these abstract rules can usually not be implemented perfectly. To find voting systems that approximate these rules the so called inverse power problem needs to be solved. I introduce a new method to address this problem in two-tier voting settings using the coefficient of variation. This method can easily be applied to a wide variety of settings and rules. After deriving the new method, I illustrate why it is to be preferred over more traditional methods. |
| Keywords: | inverse power problem, indirect voting power, two-tier voting, Penrose’s Square Root Rule |
| JEL: | D71 D72 |
| Date: | 2014–02–10 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20140019&r=gth |