Imitation Processes with Small Mutations
12 Pages Posted: 13 Nov 2004
Date Written: November 2004
This note characterizes the impact of adding rare stochastic mutations 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  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 simpler 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."
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