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Numerical Approach to Locating Multiple Equilibria of Game-theoretic Models

Student: Dmitrii Rykunov

Supervisor: Ivan Stankevich

Faculty: Faculty of Economic Sciences

Educational Programme: Economics (Bachelor)

Year of Graduation: 2017

This thesis investigates possibility to develop a general-purpose framework to numerically analyze models involving decision-making aspect in terms of system stability and individual decision-makers’ behavior. It focuses on models equivalent to finite non-cooperative games. We start with a mathematical formalization of such models and their equilibria and outline of an approach to analyze them, based on evolutionary game theory concepts. We proceed by implementation of the approach in an algorithm, inspired by evolutionary optimization algorithms, capable of locating multiple equilibria with iterated local search procedure. The algorithm’s convergence to equilibria concepts traditional for evolutionary game theory studies, namely evolutionary stable strategy and evolutionary stable set, is demonstrated both by theoretical findings and by empirical results.

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