Imitation Processes with Small Mutations

Drew Fudenberg and Lorens A. Imhof

No 2050, Harvard Institute of Economic Research Working Papers from Harvard - Institute of Economic Research

Abstract: This note characterizes the impact of adding rare stochastic muta- tions to an "imitation dynamic," meaning a process with the properties that any state where all agents use the same strategy is absorbing, and all other states are transient. The work of Freidlin and Wentzell [10] and its extensions implies that the resulting system will spend almost all of its time at the absorbing states of the no-mutation process, and provides a general algorithm for calculating the limit distribution, but this algorithm can be complicated to apply. This note provides a sim- pler and more intuitive algorithm. Loosely speaking, in a process with K strategies, it is sufficient to find the invariant distribution of a K x 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. "

Date: 2004
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Related works:
Journal Article: Imitation processes with small mutations (2006)
Working Paper: Imitation Processes with Small Mutations (2006)
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