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Yeneng Sun - One of the best experts on this subject based on the ideXlab platform.

  • Pure-Strategy equilibria in Bayesian games
    Journal of Economic Theory, 2019
    Co-Authors: Yeneng Sun
    Abstract:

    Abstract A general condition called “coarser inter-player information” is introduced and shown to be necessary and sufficient for the validity of several fundamental properties on Pure-Strategy equilibria in Bayesian games, such as existence, purification from behavioral strategies, and convergence for a sequence of games. Our sufficiency results cover various earlier results on Pure-Strategy equilibria in Bayesian games as special cases. New applications are presented as illustrative examples, including auctions with externalities and risk-neutral bidders, and Bertrand pricing games with asymmetric information.

  • Pure Strategy equilibria in games with private and public information
    Journal of Mathematical Economics, 2007
    Co-Authors: Yeneng Sun, Nicholas C. Yannelis, Zhixiang Zhang
    Abstract:

    We introduce a new game form which allows the players’ strategies to depend on their Strategy-relevant private information as well as on some publicly announced information. The players’ payoffs depend on their own payoff-relevant private information and some payoff-relevant common information. Under the assumption that the players’ Strategy-relevant private information is diffuse and their private information is conditionally independent given the public and payoff-relevant common information, we prove the existence of a Pure Strategy equilibrium for such a game by developing a distribution theory of correspondences via vector measures.

  • On a private information game without Pure Strategy equilibria1
    Journal of Mathematical Economics, 1999
    Co-Authors: M. Ali Khan, Kali P. Rath, Yeneng Sun
    Abstract:

    Abstract We present an example of a two-person game of private information in which there is no equilibrium in Pure strategies. Our example satisfies all the hypotheses of the existence theorems present in the literature on the subject of Pure Strategy equilibria, except for the fact that the action set of each player is given by the interval [−1,1]. As such, it illustrates the limitations that pertain to the purification of equilibria in a standard setting.

  • on the existence of Pure Strategy equilibria in games with a continuum of players
    Journal of Economic Theory, 1997
    Co-Authors: Ali M Khan, Kali P. Rath, Yeneng Sun
    Abstract:

    Abstract We present results on the existence of Pure Strategy Nash equilibria in nonatomic games. We also show by means of counterexamples that the stringent conditions on the cardinality of action sets cannot be relaxed, and thus resolve questions which have remained open since Schmeidler's 1973 paper. Journal of Economic Literature Classification Number: C72.

  • On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players
    Journal of Economic Theory, 1997
    Co-Authors: M. Ali Khan, Kali P. Rath, Yeneng Sun
    Abstract:

    We present results on the existence of Pure Strategy Nash equilbria in nonatomic games We also show by means of counterexamples that the stringent conditions on the cardinality of actions sets cannot be relaxed and thus resolve questions which have remained open since Schmeidler's 1973 paper

Kali P. Rath - One of the best experts on this subject based on the ideXlab platform.

Susan Athey - One of the best experts on this subject based on the ideXlab platform.

  • single crossing properties and the existence of Pure Strategy equilibria in games of incomplete information
    Econometrica, 2001
    Co-Authors: Susan Athey
    Abstract:

    This paper analyzes a class of games of incomplete information where each agent has private information about her own type, and the types are drawn from an atomless joint probability distribution. The main result establishes existence of Pure Strategy Nash equilibria (PSNE) under a condition we call the single crossing condition (SCC), roughly described as follows: whenever each opponent uses a nondecreasing Strategy (in the sense that higher types choose higher actions), a player's best response Strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite-action game. Further, for games with continuous payoffs and a continuum of actions, there exists a sequence of PSNE to finite-action games that converges to a PSNE of the continuum-action game. These convergence and existence results also extend to some classes of games with discontinuous payoffs, such as first-price auctions, where bidders may be heterogeneous and reserve prices are permitted. Finally, the paper characterizes the SCC based on properties of utility functions and probability distributions over types. Applications include first-price, multi-unit, and all-pay auctions; pricing games with incomplete information about costs; and noisy signaling games.

  • single crossing properties and the existence of Pure Strategy equilibria in games of incomplete information
    1997
    Co-Authors: Susan Athey
    Abstract:

    This paper derives sufficient conditions for a class of games of incomplete information, such as first price auctions, to have Pure Strategy Nash equilibria (PSNE). The paper treats games between two or more heterogeneous agents, each with private information about his own type (for example, a bidder's value for an object of a firm's marginal cost of production), and the types are drawn from an atomless joint probability distribution which potentially allows for correlation between types. Agents' utility may depend directly on the realizations of other agents' types, as in Milgrom and Weber's (1982) formulation of the "mineral rights" auction. The restriction we consider is that each player's expected payoffs satisfy the following single crossing condition: whenever each opponent uses a nondecreasing Strategy (that is, an opponent who has a higher type chooses a higher action), then a player's best response Strategy is also nondecreasing in her type. The paper has two main results. The first result shows that, when players are restricted to choose among a finite set of actions (for example, bidding or pricing where the smallest unit is a penny), games where players' objective functions satisfy this single crossing condition will have PSNE. The second result demonstrates that when players' utility functions are continuous, as well as in mineral rights auction games and other games where "winning" creates a discontinuity in payoffs, the existence result can be extended to the case where players choose from a continuum of actions. The paper then applies the theory to several classes of games, providing conditions on utility functions and joint distributions over types under which each class of games satisfies the single crossing condition. In particular, the single crossing condition is shown to hold in all first-price, private value auctions with potentially heterogeneous, risk-averse bidders, with either independent or affiliated values, and with reserve prices which may differ across bidders; mineral rights auctions with two heterogeneous bidders and affiliated values; a class of pricing games with incomplete information about costs; a class of all-pay auction games; and a class of noisy signaling games. Finally, the formulation of the problem introduced in this paper suggests a straightforward algorithm for numerically computing equilibrium bidding strategies in games such as first price auctions, and we present numerical analyses of several auctions under alternative assumptions about the joint distribution of types.

Hongbin Dong - One of the best experts on this subject based on the ideXlab platform.

  • mixed Strategy may outperform Pure Strategy an initial study
    Congress on Evolutionary Computation, 2013
    Co-Authors: Wei Hou, Hongbin Dong
    Abstract:

    A Pure Strategy metaheuristic is one that applies the same search method at each generation of the algorithm. A mixed Strategy metaheuristic is one that selects a search method probabilistically from a set of strategies at each generation. For example, a classical genetic algorithm, that applies mutation with probability 0.9 and crossover with probability 0.1, belong to mixed Strategy heuristics. A (1+1) evolutionary algorithm using mutation but no crossover is a Pure Strategy metaheuristic. The purpose of this paper is to compare the performance between mixed Strategy and Pure Strategy metaheuristics. The main results of the current paper are summarised as follows. (1) We construct two novel mixed Strategy evolutionary algorithms for solving the 0-1 knapsack problem. Experimental results show that the mixed Strategy algorithms may find better solutions than Pure Strategy algorithms in up to 77.8% instances through experiments. (2) We establish a sufficient and necessary condition when the expected runtime time of mixed Strategy metaheuristics is smaller that that of Pure Strategy mixed Strategy metaheuristics.

  • Mixed Strategy May Outperform Pure Strategy: An Initial Study
    2013 IEEE Congress on Evolutionary Computation, 2013
    Co-Authors: Wei Hou, Hongbin Dong
    Abstract:

    In Pure Strategy meta-heuristics, only one search Strategy is applied for all time. In mixed Strategy meta-heuristics, each time one search Strategy is chosen from a Strategy pool with a probability and then is applied. An example is classical genetic algorithms, where either a mutation or crossover operator is chosen with a probability each time. The aim of this paper is to compare the performance between mixed Strategy and Pure Strategy meta-heuristic algorithms. First an experimental study is implemented and results demonstrate that mixed Strategy evolutionary algorithms may outperform Pure Strategy evolutionary algorithms on the 0-1 knapsack problem in up to 77.8% instances. Then Complementary Strategy Theorem is rigorously proven for applying mixed Strategy at the population level. The theorem asserts that given two meta-heuristic algorithms where one uses Pure Strategy 1 and another uses Pure Strategy 2, the condition of Pure Strategy 2 being complementary to Pure Strategy 1 is sufficient and necessary if there exists a mixed Strategy meta-heuristics derived from these two Pure strategies and its expected number of generations to find an optimal solution is no more than that of using Pure Strategy 1 for any initial population, and less than that of using Pure Strategy 1 for some initial population.

  • EvoCOP - Pure Strategy or mixed Strategy
    Evolutionary Computation in Combinatorial Optimization, 2012
    Co-Authors: Hongbin Dong
    Abstract:

    Mixed Strategy evolutionary algorithms (EAs) aim at integrating several mutation operators into a single algorithm. However no analysis has been made to answer the theoretical question: whether and when is the performance of mixed Strategy EAs better than that of Pure Strategy EAs? In this paper, asymptotic convergence rate and asymptotic hitting time are proposed to measure the performance of EAs. It is proven that the asymptotic convergence rate and asymptotic hitting time of any mixed Strategy (1+1) EA consisting of several mutation operators is not worse than that of the worst Pure Strategy (1+1) EA using only one mutation operator. Furthermore it is proven that if these mutation operators are mutually complementary, then it is possible to design a mixed Strategy (1+1) EA whose performance is better than that of any Pure Strategy (1+1) EA using only one mutation operator.

  • Pure Strategy or mixed Strategy
    arXiv: Neural and Evolutionary Computing, 2011
    Co-Authors: Hongbin Dong
    Abstract:

    Mixed Strategy EAs aim to integrate several mutation operators into a single algorithm. However few theoretical analysis has been made to answer the question whether and when the performance of mixed Strategy EAs is better than that of Pure Strategy EAs. In theory, the performance of EAs can be measured by asymptotic convergence rate and asymptotic hitting time. In this paper, it is proven that given a mixed Strategy (1+1) EAs consisting of several mutation operators, its performance (asymptotic convergence rate and asymptotic hitting time)is not worse than that of the worst Pure Strategy (1+1) EA using one mutation operator; if these mutation operators are mutually complementary, then it is possible to design a mixed Strategy (1+1) EA whose performance is better than that of any Pure Strategy (1+1) EA using one mutation operator.

Wei Hou - One of the best experts on this subject based on the ideXlab platform.

  • mixed Strategy may outperform Pure Strategy an initial study
    Congress on Evolutionary Computation, 2013
    Co-Authors: Wei Hou, Hongbin Dong
    Abstract:

    A Pure Strategy metaheuristic is one that applies the same search method at each generation of the algorithm. A mixed Strategy metaheuristic is one that selects a search method probabilistically from a set of strategies at each generation. For example, a classical genetic algorithm, that applies mutation with probability 0.9 and crossover with probability 0.1, belong to mixed Strategy heuristics. A (1+1) evolutionary algorithm using mutation but no crossover is a Pure Strategy metaheuristic. The purpose of this paper is to compare the performance between mixed Strategy and Pure Strategy metaheuristics. The main results of the current paper are summarised as follows. (1) We construct two novel mixed Strategy evolutionary algorithms for solving the 0-1 knapsack problem. Experimental results show that the mixed Strategy algorithms may find better solutions than Pure Strategy algorithms in up to 77.8% instances through experiments. (2) We establish a sufficient and necessary condition when the expected runtime time of mixed Strategy metaheuristics is smaller that that of Pure Strategy mixed Strategy metaheuristics.

  • Mixed Strategy May Outperform Pure Strategy: An Initial Study
    2013 IEEE Congress on Evolutionary Computation, 2013
    Co-Authors: Wei Hou, Hongbin Dong
    Abstract:

    In Pure Strategy meta-heuristics, only one search Strategy is applied for all time. In mixed Strategy meta-heuristics, each time one search Strategy is chosen from a Strategy pool with a probability and then is applied. An example is classical genetic algorithms, where either a mutation or crossover operator is chosen with a probability each time. The aim of this paper is to compare the performance between mixed Strategy and Pure Strategy meta-heuristic algorithms. First an experimental study is implemented and results demonstrate that mixed Strategy evolutionary algorithms may outperform Pure Strategy evolutionary algorithms on the 0-1 knapsack problem in up to 77.8% instances. Then Complementary Strategy Theorem is rigorously proven for applying mixed Strategy at the population level. The theorem asserts that given two meta-heuristic algorithms where one uses Pure Strategy 1 and another uses Pure Strategy 2, the condition of Pure Strategy 2 being complementary to Pure Strategy 1 is sufficient and necessary if there exists a mixed Strategy meta-heuristics derived from these two Pure strategies and its expected number of generations to find an optimal solution is no more than that of using Pure Strategy 1 for any initial population, and less than that of using Pure Strategy 1 for some initial population.

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