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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
Checking that finite state concurrent programs satisfy their linear specification
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
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)
Environment Assumptions for Synthesis
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
ATL with Strategy Contexts and Bounded Memory
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Equilibria in quantitative reachability games
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Synthesizing protocols for digital contract signing
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Subgame perfection for equilibria in quantitative reachability games
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
A theory of agreements and protection
POST'13 Proceedings of the Second international conference on Principles of Security and Trust
On Equilibria in Quantitative Games with Reachability/Safety Objectives
Theory of Computing Systems
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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 sometimes 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.