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). Harvard Institute of Economic Research Discussion Paper No. 2050. 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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