On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The temporal logic of reactive and concurrent systems
The temporal logic of reactive and concurrent systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
Languages, automata, and logic
Handbook of formal languages, vol. 3
Formal Methods in System Design - Special issue on The First Federated Logic Conference (FLOC'96), part II
Alternating-time temporal logic
Journal of the ACM (JACM)
How much memory is needed to win infinite games?
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
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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 winning conditions, which include the games that arise in verification, there may be several Nash equilibria, but there is always a unique maximal payoff profile of a secure equilibrium. We show how this equilibrium can be computed in the case of ω-regular winning conditions, and we characterize the memory requirements of strategies that achieve the equilibrium.