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Title: Equilibria of Large Games and Bayesian Games with private and public information
Keywords: Equilibria; Large Games; Bayesian Games
Issue Date: 10-Jul-2008
Citation: FU HAIFENG (2008-07-10). Equilibria of Large Games and Bayesian Games with private and public information. ScholarBank@NUS Repository.
Abstract: This thesis studies the equilibria in large games and Bayesian games and it consists of four parts. Firstly, we generalize the traditional Bayesian games by introducing a new Bayesian game with private and public information. This new game model allows the players' strategies to depend on their private information and on some publicly announced information. Under the regularity assumptions, we directly prove the existence of pure strategy equilibrium for such a game by developing a distribution theory of correspondences via vector measures. Secondly, we show the existence of mixed-strategy equilibria in such games under more general conditions. Moreover, under some regularity conditions, a strong purification result is obtained for the mixed strategies in such games. As a corollary, the existence of pure-strategy equilibria follows. Thirdly, we consider a generalized large game model where the agent space is divided into countable subgroups. Focusing on the interaction between Nash equilibria and the best response correspondence of the players, we characterize the pure-strategy equilibrium distributions in three different settings of large games. Furthermore, we also present a counterexample for a more general setting. In the last part, we present a unified proof for the existence of pure strategy equilibria in the three settings of large games mentioned above. Then we show that each Bayesian game can induce a large game and the Bayesian game has a pure strategy equilibria if and only if the induced large game has one. This result enables us to apply the existence results in large games to Bayesian games and obtain existence of pure strategy equilibria in four different settings of Bayesian games.
Appears in Collections:Ph.D Theses (Open)

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