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List of Discussion Paper Series
- No.2002-02 (June 2002)
- Stochastic Pathwise Approach to Imitational Behavior
- Yasuo TANABE (Associate Professor, Faculty of Economics, Nagasaki University)
- Abstract:
- We study the imitational behavior, that is, learning or imitation of each individual in a multi-population game when the population state converges to an equilibrium state. Our study is based on the pathwise analysis of a continuous time Markov chain that completely describes the imitational behavior of each individual.
We show that all individuals settle on a pure strategy in the long run if and only if the pure strategy is a best reply to the limit state. Moreover, all individuals’ time average of holding each strategy become equalized to the weight of the strategy at the limit state to which the population state converges, because their schemes of imitational behavior go to the same. Our results assert that it is inappropriate to reason about each individual’s imitational behavior in the population based only on the convergence of the population state.
- Keywords:
- imitational behavior, propagation of chaos, Mckean process, elimination of strategy,ergodicity, equalization.
- JEL Classification:
- C72,C79.