Imitation processes with small mutations

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 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. (c) 2005 Elsevier Inc. All rights reserved.