The purpose of this paper is two-fold: The first is to propose a dynamic model for describing rough reasoning decision making. The second is to show that involvement of some irrational decision makers in society may lead to high social welfare by analyzing the centipede game in the framework of the model. In perfect information games, though it is theoretically able to calculate reasonable equilibria precisely by backward induction, it is practically difficult to realize them. In order to capture such features, we first develop a dynamic model assuming explicitly that the players may make mistakes due to rough reasoning. Next, we will apply it to the centipede game. Our findings include there is a case that neither random nor completely rational, moderate rational society maximize the frequency of cooperative behaviors. This result suggests that society involving some rough reasoning decision-makers may lead to socially more desirable welfare, compared to completely rational society.
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