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Regret-Based Nash Equilibrium Sorting Genetic Algorithm for Combinatorial Game Theory Problems with Multiple Players.

Abdullah Konak1, Sadan Kulturel-Konak2

  • 1Information Sciences and Technology, Penn State Berks, Reading, PA, 19610, USA auk3@psu.edu.

Evolutionary Computation
|March 1, 2022
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Summary
This summary is machine-generated.

We developed a novel regret-based strategy for evolutionary algorithms to find Nash equilibria in complex games. This approach, Regret-Based Nash Equilibrium Sorting Genetic Algorithm (RNESGA), effectively guides search toward equilibria in intractable combinatorial game theory problems.

Keywords:
Genetic algorithmsevolution strategiesgame theory

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Area of Science:

  • Game Theory
  • Artificial Intelligence
  • Computational Complexity

Background:

  • Evolutionary algorithms (EAs) face challenges in finding Nash equilibria in noncooperative simultaneous games, particularly when decision spaces are vast.
  • Existing methods struggle to guide EAs toward equilibria, which are often suboptimal points in the objective landscape.
  • Computational intractability in enumerating player options limits EA applications in complex combinatorial games.

Purpose of the Study:

  • To introduce a novel regret-based fitness assignment strategy for EAs to efficiently identify Nash equilibria.
  • To address the limitations of current EAs in navigating the objective space towards equilibrium points.
  • To enhance the applicability of EAs to noncooperative simultaneous combinatorial games.

Main Methods:

  • Proposed a multipopulation genetic algorithm named Regret-Based Nash Equilibrium Sorting Genetic Algorithm (RNESGA).
  • Implemented a regret-based fitness assignment strategy to select candidate decision options for the next generation.
  • Utilized competitive knapsack games and other established game theory problems for evaluation.

Main Results:

  • RNESGA demonstrated the capability to converge to multiple Nash equilibria within a single execution.
  • The strategy proved effective in two- and three-player competitive knapsack games.
  • Pure payoff-based fitness assignment strategies exhibited poor performance in three-player game scenarios.

Conclusions:

  • Regret-based fitness assignment is a viable strategy for evolutionary algorithms to find Nash equilibria in complex games.
  • RNESGA offers an effective method for discovering multiple equilibria in a single run, overcoming previous limitations.
  • The findings highlight the inadequacy of simple payoff-based strategies in multi-player, complex game theory problems.