|
on Game Theory |
| By: | Liu, Qingmin (University of Pennsylvania); Skrzypacz, Andrzej (Stanford University) |
| Abstract: | We study the impact of limited records on reputation dynamics, that is, how the set of equilibria and equilibrium payoffs changes in a model in which one long-lived player faces a sequence of short-lived players who observe only limited information about past play (the last K periods of the long-lived player's actions). We show that limited records dramatically change the equilibrium behavior. Moreover, with limited records, equilibria in games with complete and incomplete information are strikingly different (in contrast to games with complete records). We also obtain a lower bound for equilibrium payoffs at any moment of the game, not only at the beginning, thus providing a stronger long-run prediction. |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:2030&r=gth |
| By: | Duersch, Peter (University of Heidelberg); Oechssler, Jorg (University of Heidelberg); Schipper, Burkhard C. (University of California, Davis) |
| Abstract: | It is well known that the rock-paper-scissors game has no pure saddle point. We |
| Abstract: | show that this holds more generally: A symmetric two-player zero-sum game has |
| Abstract: | a pure saddle point if and only if it is not a generalized rock-paper-scissors game. |
| Abstract: | Moreover, we show that every finite symmetric quasiconcave two-player zero-sum |
| Abstract: | game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the |
| Abstract: | class of symmetric two-player zero-sum games coincides with the class of relative |
| Abstract: | payoff games associated with symmetric two-player games. This allows us to derive |
| Abstract: | results on the existence of a finite population evolutionary stable strategies. |
| JEL: | C72 C73 |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:ucdeco:10-4&r=gth |
| By: | László Á. Kóczy (Óbuda University) |
| Abstract: | While they use the language of game theory the known measures of a priory voting power are hardly more than statistical expectations assuming the random behaviour of the players. Focusing on normalised indices we show that rational players would behave dierently from the indices' predictions and propose a model that captures such strategic behaviour. In our model players do not automatically participate in every winning coalition they are members of, but have the possibility to block the formation of such a coalition. The strategic use of such blocks can increase voting power, when the latter is dened over the game with the remaining winning coalitions. In our model players do not automatically participate in every winning coalition they are members of, but have the possibility to block the formation of such a coalition. The strategic use of such blocks can increase voting power, when the latter is defined over the game with the remaining winning coalitions. |
| Keywords: | Banzhaf index, Shapley-Shubik index, a priori voting power, rational players. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:pkk:wpaper:1001.rdf&r=gth |
| By: | Fabien Lange (Óbuda University); László Á. Kóczy (Óbuda University) |
| Abstract: | A voting situation is given by a set of voters and the rules of legislation that determine minimal requirements for a group of voters to pass a motion. A priori measures of voting power, such as the Shapley-Shubik index and the Banzhaf value, show the influence of the individual players. We used to calculate them by looking at marginal contributions in a simple game consisting of winning and losing coalitions derived from the rules of the legislation. We introduce a new way to calculate these measures directly from the set of minimal winning coalitions. This new approach logically appealing as it writes measures as functions of the rules of the legislation. For certain classes of games that arise naturally in applications the logical shortcut drastically simplifies calculations. The technique generalises directly to all semivalues. Keywords. Shapley-Shubik index, Banzhaf index, semivalue, minimal winning coalition, Möbius transform. |
| Keywords: | Shapley-Shubik index, Banzhaf index, semivalue, minimal winning coalition, Möbius transform. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:pkk:wpaper:1002.rdf&r=gth |
| By: | Grégoire ROTA-GRAZIOSI (Centre d'Etudes et de Recherches sur le Développement International); Magnus HOFFMANN |
| Abstract: | The aim of this paper is to generalize the endogenous timing game proposed by Hamilton and Slutsky (1990) to cases where the reaction functions are non-motononic, as for instance in the literature on contest. Following the taxonomy of social dilemma provided by Eaton (2004) we consider several pos- sible situations depending on the nature of interactions (plain complementarity or plain substituability and strategic complementarity or strategic substitutability). Under the assumptions of the existence and the uniqueness of the Nash and Stackelberg equilibria, we highlight the presence of a ï¬rst-mover advantage or a second-mover incentive only depending on the nature of cross-effects in players' payoff functions and the slopes of their reaction functions at the Nash equilibrium of the static game. These properties allow us to determine rigorously the Subgame Perfect Nash Equilibrium (SPNE) in the ten studied situations. We establish under which conditions on the nature of interactions a leader emerges at the SPNE |
| Keywords: | ï¬rst-mover advantage, endogenous timing game, second-mover incentive, Subgame Perfect Nash Equilibrium |
| JEL: | L13 D43 C72 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:cdi:wpaper:1167&r=gth |
| By: | Daniel Jaume; Jordi Massó; Alejandro Neme |
| Abstract: | A multiple-partners assignment game with heterogeneous sells and multi-unit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by only using linear programming. We show that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all equilibrium assignments, and vice versa. We also show that the set of (restricted) equilibrium price vectors has a natural lattice structure and we study how this structure is translated into the set of agents' utilities that are attainable at equilibrium. |
| Keywords: | Matching, Assignment Game, Indivisible Goods, Competitive Equilibrium, Lattice |
| JEL: | C78 D78 |
| Date: | 2009–07–26 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:802.09&r=gth |
| By: | Duersch, Peter (University of Heidelberg); Oechssler, Jorg (University of Heidelberg); Schipper, Burkhard C. (University of California, Davis) |
| Abstract: | We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly, price competition, rent seeking, public goods games, common pool resource games, minimum effort coordination games, arms race, search, bargaining, etc., imitation cannot be beaten by much even by a very clever opponent |
| JEL: | C72 C73 D43 |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:ucdeco:10-3&r=gth |
| By: | Wu, Haoyang |
| Abstract: | [E. Maskin, \emph{Rev. Econom. Stud.} \textbf{66} (1999) 23-38] is a seminal paper in the field of mechanism design and implementation theory. [J. Moore and R. Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099] and [B. Dutta and A. Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128] are two fundamental papers on two-player Nash implementation. Recently, [H. Wu, http://arxiv.org/pdf/1004.5327v1 ] proposed a classical algorithm to break through Maskin's theorem for the case of many agents. In this paper, we will give two examples to break through the aforementioned results on two-agent Nash implementation by virtue of Wu's algorithm. There are two main contributions of this paper: 1) A two-player social choice rule (SCR) that satisfies Condition $\mu2$ cannot be Nash implemented if an additional Condition $\lambda'$ is satisfied. 2) A non-dictatorial two-player weakly pareto-optimal SCR is Nash implementable if Condition $\lambda'$ is satisfied. Although the former is negative for the economic society, the latter is just positive. Put in other words, some SCRs which are traditionally viewed as not be Nash implementable may be Nash implemented now. |
| Keywords: | Quantum games; Mechanism design; Implementation theory; Nash implementation; Maskin monotonicity. |
| JEL: | D71 C72 |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:22670&r=gth |
| By: | Miyazaki, Kentaro; Takekuma, Shin-Ichi |
| Abstract: | Exchange economies in which preferences of some consumers are possibly satiated are considered. In a general model of an atomless exchange economy, the equivalence between the ‘rejective’ core and the set of dividend equilibrium allocations is proved by applying Liapunov’s theorem in multi-dimensions. |
| Keywords: | rejective core, dividend equilibrium, core equivalence |
| JEL: | C71 D41 D51 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2010-05&r=gth |
| By: | Koichi Tadenuma |
| Abstract: | In two-sided matching problems, we consider "natural" changes in prefer- ences of agents in which only the rankings of current partners are enhanced. We introduce two desirable properties of matching rules under such rank- enhancements of partners. One property requires that an agent who be- comes higher ranked by the original partner should not be punished. We show that this property cannot always be met if the matchings are required to be stable. However, if only one agent changes his preferences, the above requirement is compatible with stability, and moreover, envy-minimization in stable matchings can also be attained. The other property is a solidarity property, requiring that all of the "irrelevant" agents, whose preferences as well as whose original partners' preferences are unchanged, should be affected in the same way; either all weakly better off or all worse off. We show that when matchings are required to be stable, this property does not always hold. |
| Keywords: | two-sided matching problem, stable matching, partnership, solidarity |
| JEL: | C78 C71 D71 D63 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:hst:ghsdps:gd10-137&r=gth |
| By: | Ruth Martínez; Jordi Massó; Alejandro Neme; Jorge Oviedo |
| Abstract: | We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set of preference profiles into subsets with the property that all preference profiles in the same subset have the same Core. We also show how to identify a profile of (incomplete) binary relations containing the minimal information needed to generate as strict extensions all the (complete) preference profiles with the same Core. This is important for applications since it reduces the amount of information that agents have to reveal about their preference relations to centralized Core matching mechanisms; moreover, this reduction is maximal. |
| Keywords: | Matching, Core |
| JEL: | C78 |
| Date: | 2009–07–26 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:803.09&r=gth |
| By: | Salvador Barberà |
| Abstract: | This paper surveys the literature on strategy-proofness from a historical perspective. While I discuss the connections with other works on incentives in mechanism design, the main emphasis is on social choice models. This article has been prepared for the Handbook of Social Choice and Welfare, Volume 2, Edited by K. Arrow, A. Sen and K. Suzumura |
| Keywords: | Strategy-proofness, Social Choice, Dominant Strategies, Domain Restrictions, Voting |
| JEL: | D7 D51 C7 H41 |
| Date: | 2010–01–19 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:828.10&r=gth |
| By: | Baron, David P. (Stanford University); Hirsch, Alexander V. (Stanford University) |
| Abstract: | This paper presents a theory of common agency lobbying in which policy-interested lobbies can first influence the choice of a governing coalition and then influence the legislative bargaining over policies. Equilibria can involve active lobbying at both stages of the governing process. Contributions can also be made to defeat a policy proposal, and although those contributions are never successful they can influence coalition choice. The equilibrium policy in the legislative bargaining stage is efficient given the coalition selected, but the equilibrium coalition need not be efficient. Lobbying can also lead to the preservation of the status quo and lobby-induced gridlock. An example is presented to identify the multiplicity of equilibria and provide a full characterization of an equilibrium. |
| Date: | 2009–07 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:2031&r=gth |
| By: | Hatfield, John William (Stanford University); Kominers, Scott Duke (Harvard University) |
| Abstract: | We introduce a model in which firms trade goods via bilateral contracts which specify a buyer, a seller, and the terms of the exchange. This setting subsumes (many-to- many) matching with contracts, as well as supply chain matching. When firms' relationships do not exhibit a supply chain structure, stable allocations need not exist. By contrast, in the presence of supply chain structure, a natural substitutability condition characterizes the maximal domain of firm preferences for which stable allocations always exist. Furthermore, the classical lattice structure, rural hospitals theorem, and one-sided strategy-proofness results all generalize to this setting. |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:2050&r=gth |
| By: | Santiago Sanchez-Pages |
| Abstract: | This paper studies bargaining and conflict under incomplete information, provides an overview and a critical account of the literature on the topic and contributes with original research. We first revise models of mechanism design and sequential bargaining that take confrontation as final. Conflict and inefficiencies are to be expected in these models whenever parties have optimistic prospects on the outcome of the all-out conflict. After examining the causes and reasons for this optimism, we move to the analysis of the recent literature that considers the existence of limited confrontations that allow bargaining to resume. In the presence of private information, these limited conflicts convey information and thus become a bargaining instrument. The paper closes with a discussion on the related empirical literature, the challenges that it faces and some potential avenues for further research. |
| Keywords: | Bargaining, Conflict, Incomplete information, Power, Optimism, Hicks paradox, Uneven contenders paradox. |
| JEL: | C78 D74 D82 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:edn:esedps:191&r=gth |
| By: | Leandro Arozamena (Universidad Torcuato Di Tella & CONICET); Federico Weinschelbaum (Department of Economics, Universidad de San Andres) |
| Abstract: | We examine the problem of endogenous entry in a single-unit auction when the seller's welfare depends positively on the utility of a subset of potential bidders. We show that, unless the seller values those bidders?welfare more than her own ?private?utility, a nondiscriminatory auction is optimal. |
| Keywords: | auctions, favoritism, free entry, endogenous number of bidders |
| JEL: | C72 D44 |
| Date: | 2010–05 |
| URL: | http://d.repec.org/n?u=RePEc:sad:wpaper:103&r=gth |
| By: | Schipper, Burkhard (University of California, Davis) |
| Abstract: | I develop awareness-dependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2009) as primitives in the Anscombe-Aumann approach to subjective expected utility. I observe that a decision maker is unaware of an event if and only if her choices reveal that the event is "null" and the negation of the event is "null". Moreover, I characterize "impersonal" expected utility that is behaviorally indistinguishable from awareness-dependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. I discuss in what sense impersonal expected utility can not represent unawareness. |
| JEL: | C70 C72 D80 D82 |
| Date: | 2010–03 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:ucdeco:10-5&r=gth |