Issues on Strategy-Switching Dynamics
In many economic dynamic models, economic agents rationally and constantly switch to more profitable strategies in response to the outcomes as well as the environments.1 In most cases with finite agents, the payoff for adopting an optimal strategy by each agent depends not only on the strategies space but also on the frequency with which different strategies are adopted. A strategy that is relatively superior to the others in a particular distribution can turn inferior in other distributions. The nonexistence of a strategy, that is superior to all other strategies for all distributions, forces rational agents to switch their strategies now and then in response to changing frequency. In other words, economic agents “migrate” constantly among the different strategy groups.
In such a set-up, the traditional concept of static equilibrium frequency (at which agents in different strategy groups have identical benefits) is not applicable in determining the final outcome of strategy-switching dynamics, for the reason that certain variation may improve some agents’ payoffs and hence induce the “migration trend”. Such “migration” continues until none of them have incentive to change further, a state of dynamic equilibrium, at which the profits across different strategy groups may differ significantly.
KeywordsStrategy Group Competitive Equilibrium Stable Distribution Evolutionary Stable Strategy Stable Cluster
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The research is partly supported by the research grant RG68/06 from the Ministry of Education of Singapore. I would like to thank an anonymous referee, Barkley Rosser Jr., Carl Chiarella, Laura Gardini, Gian-Italo Bischi, Volker Bohm and the participants of MDEF 2008 for positive comments and suggestions.