Imitation Processes with Small Mutations

12 Pages Posted: 13 Nov 2004

See all articles by Drew Fudenberg

Drew Fudenberg

Massachusetts Institute of Technology (MIT)

Lorens A. Imhof

RWTH Aachen University - Institute of Statistics

Date Written: November 2004

Abstract

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 [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 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."

Suggested Citation

Fudenberg, Drew and Imhof, Lorens A., Imitation Processes with Small Mutations (November 2004). Available at SSRN: https://ssrn.com/abstract=619203 or http://dx.doi.org/10.2139/ssrn.619203

Drew Fudenberg (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Lorens A. Imhof

RWTH Aachen University - Institute of Statistics ( email )

Aachen, D-52056
Germany

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