Imitation Processes with Small Mutations
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CitationFudenberg, Drew, and Lorens A. Imhof. 2006. Imitation processes with small mutations. Journal of Economic Theory 131, no. 1: 251-262.
AbstractThis note characterizes the impact of adding rare stochastic mutations to an “imitation dynamic,” meaning a process with the properties that absent strategies remain absent, and non-homogeneous states are transient. The resulting system will spend almost all of its time at the absorbing states of the no-mutation process. The work of Freidlin and Wentzell [Random Perturbations of Dynamical Systems, Springer, New York, 1984] and its extensions provide a general algorithm for calculating the limit distribution, but this algorithm can be complicated to apply. This note provides a simpler and more intuitive algorithm. Loosely speaking, in a process with K strategies, it is sufficient to find the invariant distribution of a K×K Markov matrix on the K homogeneous states, where the probability of a transit from “all play i” to “all play j” is the probability of a transition from the state “all agents but 1 play i, 1 plays j” to the state “all play j”.
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:3190369
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