190,804 research outputs found

    Best Response Equivalence

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    Two games are best-response equivalent if they have the same best-response correspondence. We provide a characterization of when two games are best-response equivalent. The characterizations exploit a dual relationship between payoff differences and beliefs. Some "potential game" arguments (cf. Monderer and Shapley, 1996, Games. Econ. Behav. 14, 124-143) rely only on the property that potential games are best-response equivalent to identical interest games. Our results show that a large class of games are best-response equivalent to identical interest games, but are not potential games. Thus we show how some existing potential game arguments can be extended.Best response equivalence; Duality; Farkas' Lemma; Potential games

    Best Response Equivalence

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    Two games are best-response equivalent if they have the same best-response correspondence. We provide a characterization of when two games are best-response equivalent. The characterizations exploit a dual relationship between payoff differences and beliefs. Some “potential game” arguments (cf. Monderer and Shapley, 1996, Games. Econ. Behav. 14, 124-143) rely only on the property that potential games are best-response equivalent to identical interest games. Our results show that a large class of games are best-response equivalent to identical interest games, but are not potential games. Thus we show how some existing potential game arguments can be extended

    A Note on the Equivalence of Rationalizability Concepts in Generalized Nice Games

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    Moulin (1984) describes the class of nice games for which the solution concept of point-rationalizability coincides with iterated elimination of strongly dominated strategies. As a consequence nice games have the desirable property that all rationalizability concepts determine the same strategic solution. However, nice games are characterized by rather strong assumptions. For example, only single-valued best responses are admitted and the individual strategy sets have to be convex and compact subsets of the real line R1. This note shows that equivalence of all rationalizability concepts can be extended to multi-valued best response correspondences. The surprising finding is that equivalence does not hold for individual strategy sets that are compact and convex subsets of Rn with n>1.

    The Equivalence of Contests

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    We use a Tullock-type contest model to show that intuitively and structurally different contests can be strategically and revenue equivalent to each other. We consider a two-player contest, where outcome-contingent payoffs are linear functions of prizes, own effort, and the effort of the rival. We identify strategically equivalent contests that generate the same family of best response functions and, as a result, the same revenue. However, two strategically equivalent contests may yield different equilibrium payoffs. Finally, we discuss possible contest design applications and avenues for future theoretical and empirical research.rent-seeking, contest, spillover, equivalence, revenue equivalence, contest design

    Equivalence between best responses and undominated

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    For games with expected utility maximizing players whose strategy sets are finite, Pearce (1984) shows that a strategy is strictly dominated by some mixed strategy, if and only if, this strategy is not a best response to some belief about opponents' strategy choice. This note generalizes Pearce's (1984) equivalence result to games with expected utility maximizing players whose strategy sets are arbitrary compact sets.

    Equivalence between best responses and undominated strategies: a generalization from finite to compact strategy sets.

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    For games with expected utility maximizing players whose strategy sets are finite, Pearce (1984) shows that a strategy is strictly dominated by some mixed strategy, if and only if, this strategy is not a best response to some belief about opponents' strategy choice. This note generalizes Pearce''s (1984) equivalence result to games with expected utility maximizing players whose strategy sets are arbitrary compact sets.

    Categorization and correlation in a random-matching game

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    We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player is a best response to the distribution of actions of his opponents in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game.Random-matching game; Categorization; Correlated equilibrium

    On Robustness Properties in Empirical Centroid Fictitious Play

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    Empirical Centroid Fictitious Play (ECFP) is a generalization of the well-known Fictitious Play (FP) algorithm designed for implementation in large-scale games. In ECFP, the set of players is subdivided into equivalence classes with players in the same class possessing similar properties. Players choose a next-stage action by tracking and responding to aggregate statistics related to each equivalence class. This setup alleviates the difficult task of tracking and responding to the statistical behavior of every individual player, as is the case in traditional FP. Aside from ECFP, many useful modifications have been proposed to classical FP, e.g., rules allowing for network-based implementation, increased computational efficiency, and stronger forms of learning. Such modifications tend to be of great practical value; however, their effectiveness relies heavily on two fundamental properties of FP: robustness to alterations in the empirical distribution step size process, and robustness to best-response perturbations. The main contribution of the paper is to show that similar robustness properties also hold for the ECFP algorithm. This result serves as a first step in enabling practical modifications to ECFP, similar to those already developed for FP.Comment: Submitted for publication. Initial Submission: Mar. 201

    A note on the equivalence of rationalizability concepts in generalized nice games

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    Moulin (1984) describes the class of nice games for which the solution concept of point-rationalizability coincides with iterated elimination of strongly dominated strategies. As a consequence nice games have the desirable property that all rationalizability concepts determine the same strategic solution. However, nice games are characterized by rather strong assumptions. For example, only single-valued best responses are admitted and the individual strategy sets have to be convex and compact subsets of the real line R1. This note shows that equivalence of all rationalizability concepts can be extended to multi-valued best response correspondences. The surprising finding is that equivalence does not hold for individual strategy sets that are compact and convex subsets of Rn with n≥1

    Making sense of nonequilibrium current fluctuations: A molecular motor example

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    The nonequilibrium response and fluctuations of Markovian dynamics, both near and far from equilibrium, are best understood by varying the system parameters along equivalence classes. In this note, I illustrate this approach for an analytically solvable molecular motor toy model.Comment: This paper is not intended for journal publicatio
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