Controlling conditional expectations by Zero-Determinant strategies

Zero-determinant strategies are memory-one strategies in repeated　games which unilaterally enforce linear relations between expected payoffs of　players. Recently, the concept of zero-determinant strategies was extended　to　the class of memory-n strategies with n _ 1, which enables more compli-cated control of payoffs by one player. However, what we can do by　memory-n　zero-determinant strategies is still not clear. Here, we show that memory-n　zero-determinant strategies in repeated games can be used to control condi-tional expectations of payoffs. Equivalently, they can be used to control ex-pected payoffs in biased ensembles, where a history of action pro_les with large　value of bias function is more weighted. Controlling conditional expectations　of payoffs is useful for strengthening zero-determinant strategies, because play-ers can choose conditions in such a way that only unfavorable action pro_les　to one player are contained in the conditions. We provide several examples　of memory-n zero-determinant strategies in the repeated prisoner's dilemma　game. We also explain that a deformed version of zero-determinant strategies　is easily extended to the memory-n case.

Creators Ueda Masahiko

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[isIdenticalTo] https://doi.org/10.1007/s43069-022-00159-3

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