Imitation Processes with Small Mutations
Abstract
This note characterizes the impact of adding rare stochastic muta- tions 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 sim- pler 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. "Download Info
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Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 2050.Length:
Date of creation: 2004
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Handle: RePEc:fth:harver:2050
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Keywords:Other versions of this item:
- Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
- Imhof, Lorens & Fudenberg, Drew, 2006. "Imitation Processes with Small Mutations," Scholarly Articles 3190369, Harvard University Department of Economics.
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Imhof, Lorens & Ellison, Glenn & Fudenberg, Drew, 2009.
"Random Matching in Adaptive Dynamics,"
Scholarly Articles
3190371, Harvard University Department of Economics.
- Ellison, Glenn & Fudenberg, Drew & Imhof, Lorens A., 2009. "Random matching in adaptive dynamics," Games and Economic Behavior, Elsevier, vol. 66(1), pages 98-114, May.
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- Matthey, Astrid, 2010.
"Imitation with intention and memory: An experiment,"
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- Astrid Matthey, 2006. "Imitation with Intention and Memory: an Experiment," SFB 649 Discussion Papers SFB649DP2006-088, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Matthijs van Veelen, 2010. "But Some Neutrally Stable Strategies are More Neutrally Stable than Others," Tinbergen Institute Discussion Papers 10-033/1, Tinbergen Institute.
- Fudenberg, Drew & Imhof, Lorens A., 2008.
"Monotone imitation dynamics in large populations,"
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- Imhof, Lorens & Fudenberg, Drew, 2008. "Monotone Imitation Dynamics in Large Populations," Scholarly Articles 3196338, Harvard University Department of Economics.
- Cui, Zhiwei & Zhai, Jian, 2010. "Escape dynamics and equilibria selection by iterative cycle decomposition," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1015-1029, November.
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