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Title:Stochastic stability of replicator dynamics with random jumps
Author(s):Vlasic, Andrew
Director of Research:Muncaster, Robert G.; Song, Renming
Doctoral Committee Chair(s):Bauer, Robert
Doctoral Committee Member(s):Muncaster, Robert G.; Song, Renming; Rapti, Zoi
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Asymptotic stochastic stability
evolutionarily stable strategy
invariant measure
Lyapunov function
Nash equilibrium
recurrence
stochastic differential equation
Abstract:We further generalize the stochastic version of the replicator dynamics due to Fudenberg and Harris. In particular, we add a random jump term to the payo ff function to simulate anomalous events and their e ffects on the fi tness. Assuming a 2 by 2 game and using a particular characteristic of the jump functions we are able to estimate the ergodic measure for all games. Lastly, working with results and methods developed by Imhoff, we prove some stability theorems for an arbitrary n by n game.
Issue Date:2012-09-18
URI:http://hdl.handle.net/2142/34446
Rights Information:Copyright 2012 Andrew Vlasic
Date Available in IDEALS:2012-09-18
2014-09-18
Date Deposited:2012-08


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