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Nash ϵ -equilibria for stochastic games with total reward functions: an approach through Markov decision processes

Francisco J. González-Padilla, Raúl Montes-de-Oca (2019)

Kybernetika

The main objective of this paper is to find structural conditions under which a stochastic game between two players with total reward functions has an ϵ -equilibrium. To reach this goal, the results of Markov decision processes are used to find ϵ -optimal strategies for each player and then the correspondence of a better answer as well as a more general version of Kakutani’s Fixed Point Theorem to obtain the ϵ -equilibrium mentioned. Moreover, two examples to illustrate the theory developed are presented....

Note: The Smallest Nonevasive Graph Property

Michał Adamaszek (2014)

Discussiones Mathematicae Graph Theory

A property of n-vertex graphs is called evasive if every algorithm testing this property by asking questions of the form “is there an edge between vertices u and v” requires, in the worst case, to ask about all pairs of vertices. Most “natural” graph properties are either evasive or conjectured to be such, and of the few examples of nontrivial nonevasive properties scattered in the literature the smallest one has n = 6. We exhibit a nontrivial, nonevasive property of 5-vertex graphs and show that...

Permissive strategies : from parity games to safety games

Julien Bernet, David Janin, Igor Walukiewicz (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem of finding...

Permissive strategies: from parity games to safety games

Julien Bernet, David Janin, Igor Walukiewicz (2010)

RAIRO - Theoretical Informatics and Applications

It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem...

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