Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Solving Pushdown Games with a Sigma3 Winning Condition
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Discounting the future in systems theory
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Optimal Strategy Synthesis in Request-Response Games
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
A Survey of Stochastic Games with Limsup and Liminf Objectives
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Pure stationary optimal strategies in Markov decision processes
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Computing game values for crash games
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Exploring the boundary of half positionality
CLIMA'10 Proceedings of the 11th international conference on Computational logic in multi-agent systems
On memoryless quantitative objectives
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Exploring the boundary of half-positionality
Annals of Mathematics and Artificial Intelligence
Deterministic priority mean-payoff games as limits of discounted games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Half-Positional determinacy of infinite games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Theoretical Computer Science
Omega-regular half-positional winning conditions
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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Reactive systems are often modelled as two person antagonistic games where one player represents the system while his adversary represents the environment. Undoubtedly, the most popular games in this context are parity games and their cousins (Rabin, Streett and Muller games). Recently however also games with other types of payments, like discounted or mean-payoff [5,6], previously used only in economic context, entered into the area of system modelling and verification. The most outstanding property of parity, mean-payoff and discounted games is the existence of optimal positional (memoryless) strategies for both players. This observation raises two questions: (1) can we characterise the family of payoff mappings for which there always exist optimal positional strategies for both players and (2) are there other payoff mappings with practical or theoretical interest and admitting optimal positional strategies. This paper provides a complete answer to the first question by presenting a simple necessary and sufficient condition on payoff mapping guaranteeing the existence of optimal positional strategies. As a corollary to this result we show the following remarkable property of payoff mappings: if both players have optimal positional strategies when playing solitary one-player games then also they have optimal positional strategies for two-player games.