Stochastic stability of replicator dynamics with random jumps

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2012

Author dc:creator

• Vlasic, Andrew

Contributors dc:contributor

• Muncaster, Robert G.
• Song, Renming
• Bauer, Robert
• Rapti, Zoi

• Asymptotic stochastic stability
• evolutionarily stable strategy
• invariant measure
• Lyapunov function
• Nash equilibrium
• recurrence
• stochastic differential equation

Statement dc:rights

• Copyright 2012 Andrew Vlasic

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/34446

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/34446