Existence and Uniqueness of Maximal Reductions Under Iterated Strict Dominance
研究迭代剔除严格劣策略的次序依赖问题，指出若最佳反应定义良好则不会出现伪纳什均衡，若策略空间紧且收益函数上半连续则次序无关，若策略集紧且收益函数连续则存在唯一非空最大缩减。
Iterated elimination of strictly dominated strategies is an order dependent procedure. It can also generate spurious Nash equilibria, fail to converge in countable steps, or converge to empty strategy sets. If best replies are well–defined, then spurious Nash equilibria cannot appear; if strategy spaces are compact and payoff functions are uppersemicontinuous in own strategies, then order does not matter; if strategy sets are compact and payoff functions are continuous in all strategies, then a unique and nonempty maximal reduction exists. These positive results extend neither to the better–reply secure games for which Reny has established the existence of a Nash equilibrium, nor to games in which (under iterated eliminations) any dominated strategy has an undominated dominator.