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Order of limits in reputations

机译：名誉限制顺序

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摘要

The fact that small departures from complete information might have large effects on the set of equilibrium payoffs draws interest in the adverse selection approach to study reputations in repeated games. It is well known that these large effects on the set of equilibrium payoffs rely on long-run players being arbitrarily patient. We study reputation games where a long-run player plays a fixed stage-game against an infinite sequence of short-run players under imperfect public monitoring. We show that in such games, introducing arbitrarily small incomplete information does not open the possibility of new equilibrium payoffs far from the complete information equilibrium payoff set. This holds true no matter how patient the long-run player is, as long as her discount factor is fixed. This result highlights the fact that the aforementioned large effects arise due to an order of limits argument, as anticipated.
机译：偏离完整信息的情况可能对均衡收益集产生重大影响的事实引起了人们对反向选择方法的兴趣，该方法用于研究重复博弈中的声誉。众所周知，这些对均衡收益集的巨大影响依赖于长期的参与者任意忍受。我们研究声誉游戏，其中长期玩家在不完善的公众监督下与无限数量的短期玩家进行固定的阶段游戏。我们证明，在此类博弈中，引入任意小的不完整信息不会带来远离完整信息均衡收益集的新均衡收益的可能性。只要长期折扣玩家的折扣系数是固定的，无论长期耐心多久，这都是正确的。该结果突出了这样一个事实，即，如预期的那样，由于顺序限制的论证而产生了上述较大的影响。

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