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We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover , we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. Our findings extend to general… (More)

We show that for many classes of symmetric two-player games, the simple decision rule " imitate-the-best " can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. cannot be beaten by much… (More)

Two rationality arguments are used to justify the link between conditional and unconditional preferences in decision theory: dynamic consistency and consequentialism. Dynamic consistency requires that ex ante contingent choices are respected by updated preferences. Consequentialism states that only those outcomes which are still possible can matter for… (More)

We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but also imitate-the-best and imitate-if-better. Every decision rule… (More)

It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further… (More)

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