Bounded Rationality of Restricted Turing Machines

8 years 1 days ago

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Bounded rationality aims to understand the eﬀects of how limited rationality aﬀects decisionmaking. The traditional models in game theory and multiagent system research, such as ﬁnite automata or unrestricted Turing machine, fall short of capturing how intelligent agents make decision in realistic applications. To address this problem, we model bounded rational agents as restricted Turing machines: restrictions on running time and on storage space. We then study our model in two-person repeated games. In the case where the running time of Turing machines is restricted, we show that computing the best response of a given strategy is much harder than the strategy itself. In the case where the storage space of the Turing machines is restricted, we show the best response of a space restricted strategy can not be implemented by machines within the same size (up to a constant factor). Finally, we study how these restrictions aﬀect the set of Nash equilibria in inﬁnitely repeated g...

Lijie Chen, Pingzhong Tang

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