We prove the existence of Bayesian Nash Equilibrium (BNE) of general-sum Bayesian games with continuous types and finite actions under the conditions that the utility functions and the prior type distributions are continuous concerning the players' types. Moreover, there exists a sequence of discretized Bayesian games whose BNE strategies converge weakly to a BNE strategy of the infinite Bayesian game. Our proof establishes a connection between the equilibria of the infinite Bayesian game and those of finite approximations, which leads to an algorithm to construct $\varepsilon$-BNE of infinite Bayesian games by discretizing players' type spaces.
翻译:我们证明巴伊西亚平面游戏(BNE)存在连续类型和有限动作的巴伊西亚普通和巴伊西亚平面游戏(BNE)的存在,条件是,在球员类型方面,通用功能和先前类型的分布是连续的。此外,还有一系列分散的巴伊西亚游戏,其BNE策略与无限巴伊亚游戏的BNE策略不甚一致。我们的证据确定了无限巴伊西亚游戏的平衡与有限近似的平衡之间的联系,这导致一种算法,通过将球员类型空间分解,构建无穷巴伊斯游戏的$varepsilon-BNE。