In 2-player non-zero-sum games, Nash equilibria capture the options for rational behavior if each player attempts to maximize her payoff. In contrast to classical game theory, we consider lexicographic objectives: first, each player tries to maximize her own payoff, and then, the player tries to minimize the opponent's payoff. Such objectives arise naturally in the verification of systems with multiple components. There, instead of proving that each component satisfies its specification no matter how the other components behave, it often suffices to prove that each component satisfies its specification provided that the other components satisfy their specifications. We say that a Nash equilibrium is secure if it is an equilibrium with respect to the lexicographic objectives of both players. We prove that in graph games with Borel objectives, which include the games that arise in verification, there may be several Nash equilibria, but there is always a unique maximal payoff profile of secure equilibria. We show how this equilibrium can be computed in the case of omega-regular objectives, and we characterize the memory requirements of strategies that achieve the equilibrium.
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LICS: Logic in Computer Science
Chatterjee K, Henzinger TA, Jurdziński M. Games with secure equilibria. In: IEEE; 2004:160-169. doi:10.1109/LICS.2004.1319610
Chatterjee, K., Henzinger, T. A., & Jurdziński, M. (2004). Games with secure equilibria (pp. 160–169). Presented at the LICS: Logic in Computer Science, IEEE. https://doi.org/10.1109/LICS.2004.1319610
Chatterjee, Krishnendu, Thomas A Henzinger, and Marcin Jurdziński. “Games with Secure Equilibria,” 160–69. IEEE, 2004. https://doi.org/10.1109/LICS.2004.1319610.
K. Chatterjee, T. A. Henzinger, and M. Jurdziński, “Games with secure equilibria,” presented at the LICS: Logic in Computer Science, 2004, pp. 160–169.
Chatterjee K, Henzinger TA, Jurdziński M. 2004. Games with secure equilibria. LICS: Logic in Computer Science 160–169.
Chatterjee, Krishnendu, et al. Games with Secure Equilibria. IEEE, 2004, pp. 160–69, doi:10.1109/LICS.2004.1319610.