Cyclic games and an algorithm to find minimax cycle means in directed graphs
USSR Computational Mathematics and Mathematical Physics
The complexity of mean payoff games on graphs
Theoretical Computer Science
Theory of hybrid systems and discrete event systems
Theory of hybrid systems and discrete event systems
Competitive Markov decision processes
Competitive Markov decision processes
Languages, automata, and logic
Handbook of formal languages, vol. 3
Alternating-time temporal logic
Journal of the ACM (JACM)
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
Games where you can play optimally without any memory
CONCUR 2005 - Concurrency Theory
On the positional determinacy of edge-labeled games
Theoretical Computer Science
Weighted automata and weighted logics
Theoretical Computer Science
From Boolean to quantitative notions of correctness
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Discounting the future in systems theory
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
ACM Transactions on Computational Logic (TOCL)
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Church synthesis problem for noisy input
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Half-Positional determinacy of infinite games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Measuring and synthesizing systems in probabilistic environments
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
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In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the limit-average or the discounted sum of the rewards along the path. Besides their simple definition, these two payoff functions enjoy the property that memoryless optimal strategies always exist. In an attempt to construct other simple payoff functions, we define a class of payoff functions which compute an (infinite) weighted average of the rewards. This new class contains both the limit-average and the discounted sum functions, and we show that they are the only members of this class which induce memoryless optimal strategies, showing that there is essentially no other simple payoff functions.