Double Oracle Algorithm for Computing Equilibria in Continuous Games

Authors

  • Lukáš Adam Faculty of Electrical Engineering, Czech Technical University in Prague
  • Rostislav Horčík Faculty of Electrical Engineering, Czech Technical University in Prague
  • Tomáš Kasl Faculty of Electrical Engineering, Czech Technical University in Prague
  • Tomáš Kroupa Faculty of Electrical Engineering, Czech Technical University in Prague

DOI:

https://doi.org/10.1609/aaai.v35i6.16641

Keywords:

Game Theory

Abstract

Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite programming. In general, however, continuous games are not directly amenable to computational procedures. In this contribution, we develop an iterative strategy generation technique for finding a Nash equilibrium in a whole class of continuous two-person zero-sum games with compact strategy sets. The procedure, which is called the double oracle algorithm, has been successfully applied to large finite games in the past. We prove the convergence of the double oracle algorithm to a Nash equilibrium. Moreover, the algorithm is guaranteed to recover an approximate equilibrium in finitely-many steps. Our numerical experiments show that it outperforms fictitious play on several examples of games appearing in the literature. In particular, we provide a detailed analysis of experiments with a version of the continuous Colonel Blotto game.

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Published

2021-05-18

How to Cite

Adam, L., Horčík, R., Kasl, T., & Kroupa, T. (2021). Double Oracle Algorithm for Computing Equilibria in Continuous Games. Proceedings of the AAAI Conference on Artificial Intelligence, 35(6), 5070-5077. https://doi.org/10.1609/aaai.v35i6.16641

Issue

Section

AAAI Technical Track on Game Theory and Economic Paradigms