Mahathi, Gunturu� and Giridhar, N S and Singh, Sanjay (2017) Fitness Function to find Game Equilibria using Genetic Algorithms. In: Sixth International Conference on Advances in Computing, Communications and Informatics (ICACCI'17), 13/09/2017, Manipal University Manipal.

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Abstract

In Non cooperative Game Theory, Nash Equilibrium can be computed by finding the best response strategy for each player. However this problem cannot be solved deterministically in polynomial time. For some finite games, there might be more than one pure strategy Game Equilibrium. In such cases, the most optimal set of solutions give the Game Equilibria. Evolutionary Algorithms and specifically Genetic Algorithms, based on Pareto dominance used in multi-objective optimization do not incorporate the Nash dominance and the extent of dominance in finding the equilibria. Many pairs of solutions do not dominate each other based on the generative relation of Pareto dominance and Nash Ascendancy. In this paper a fitness function based on the generative relation of Nash Ascendancy has been proposed to enhance the comparison of two individuals in a population. It assigns a better fitness value to pair of individuals that do not dominate each other.

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