Stochastic stability of replicator dynamics with random jumps

Vlasic, Andrew

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https://hdl.handle.net/2142/34446 Copy

Description

Title

Stochastic stability of replicator dynamics with random jumps

Author(s)

Vlasic, Andrew

Issue Date

2012-09-18T21:17:35Z

Director of Research (if dissertation) or Advisor (if thesis)

• Muncaster, Robert G.
• Song, Renming

Doctoral Committee Chair(s)

Bauer, Robert

Committee Member(s)

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

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2012-08

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

Copyright and License Information

Copyright 2012 Andrew Vlasic

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