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Games between responsive behavioural rules

Khan, Abhimanyu (2018): Games between responsive behavioural rules.

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Abstract

I study recurrent strategic interaction between two responsive behavioural rules in generic bi-matrix weakly acyclic games. The two individuals that play the game in a particular period choose their strategy by responding to a sample of strategies used by the co-players in the recent history of play. The response of a player is determined by his behavioural rule. I show that the game reaches a convention whenever the behavioural rule of each player is `weakly responsive' to the manner in which strategies were chosen in the past by the co-players, and stays locked into the convention if the behavioural rules are `mildly responsive'. Furthermore, amongst `mildly responsive' behavioural rules, individuals described by the behavioural rule of `extreme optimism' perform the best in the sense that their most preferred convention is always in the stochastically stable set; under an additional mild restriction that differentiates the behavioural rule of the other player from extreme optimism, the convention referred to above is the unique stochastically stable state.

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