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Imitation processes with small mutations

  • Fudenberg, Drew
  • Imhof, Lorens A.

This 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 jâ€.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 131 (2006)
Issue (Month): 1 (November)
Pages: 251-262

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Handle: RePEc:eee:jetheo:v:131:y:2006:i:1:p:251-262
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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