The order independence of iterated dominance in extensive games
证明，在扩展式博弈中，不同顺序的条件占优剔除虽然可能得到不同的策略组合集合，但每个玩家幸存策略之间存在映射，使得对应的策略组合导向相同的终结点。
Shimoji and Watson (1998) prove that a strategy of an extensive game is rationalizable \nin the sense of Pearce if and only if it survives the maximal elimination of conditionally dominated strategies. Briefly, this process iteratively eliminates \nconditionally dominated strategies according to a specific order, which is also the \nstart of an order of elimination of weakly dominated strategies. Since the final \nset of possible payoff profiles, or terminal nodes, surviving iterated elimination of \nweakly dominated strategies may be order-dependent, one may suspect that the \nsame holds for conditional dominance. \nWe prove that, although the sets of strategy profiles surviving two arbitrary \nelimination orders of conditional dominance may be very different from each \nother, they are equivalent in the following sense: for each player i and each pair \nof elimination orders, there exists a function φi mapping each strategy of i surviving \nthe first order to a strategy of i surviving the second order, such that, for every \nstrategy profile s surviving the first order, the profile (φi(si))i induces the same \nterminal node as s does. \nTo prove our results, we put forward a new notion of dominance and an elementary \ncharacterization of extensive-form rationalizability (EFR) that may be \nof independent interest. We also establish connections between EFR and other \nexisting iterated dominance procedures, using our notion of dominance and our \ncharacterization of EFR.