Isotone Equilibrium in Games of Incomplete Information
证明，在满足特定条件下，不完全信息博弈存在等调纯策略均衡或混合策略均衡，这些条件包括行动集为有限子格、类型多维且无原子等，并适用于超模博弈和独立类型博弈。
An isotone pure strategy equilibrium exists in any game of incomplete information in which (1) each player i's action set is a finite sublattice of multi-dimensional Euclidean space, (2) types are multidimensional and atomless, and each player's interim expected payoff function satisfies two "non-primitive conditions" whenever others adopt isotone pure strategies: (3) single-crossing in own action and type and (4) quasisupermodularity in own action.Similarly, given that ( 134) and (2') types are multi-dimensional (with atoms) an isotone mixed strategy equilibrium exists.Conditions (34) are satisfied in supermodular and log-supermodular games given affiliated types, and in games with independent types in which each player's ex post payoff satisfies (a) supermodularity in own action and (b) non-decreasing differences in own action and type.These results also extend to games with a continuum action space when each player's ex post payoff is also continuous in his and others' actions.