Imitation processes with small mutations |
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Authors: | Drew Fudenberg Lorens A Imhof |
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Institution: | aDepartment of Economics, Harvard University, Cambridge, MA 02138, USA;bDepartment of Economics, Bonn University, D-53113 Bonn, Germany |
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Abstract: | 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×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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Keywords: | Ergodic distribution Imitation dynamics Limit distribution Markov chain |
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