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Perfect-Information Stochastic Mean-Payoff Parity Games [chapter]

Krishnendu Chatterjee, Laurent Doyen, Hugo Gimbert, Youssouf Oualhadj
2014 Lecture Notes in Computer Science  
, d the number of priorities of the parity objective, and MeanGame is the complexity to compute the set of almost-sure winning states in 2 1 2 -player mean-payoff games.  ...  We consider 2 1 2 -player games where the objective of the System is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a mean-payoff  ...  Introduction Perfect-information stochastic games.  ... 
doi:10.1007/978-3-642-54830-7_14 fatcat:fgzfjysqcbdgvgfglzyw7qkpyu

Discounting Infinite Games But How and Why?

Hugo Gimbert, Wiesław Zielonka
2005 Electronical Notes in Theoretical Computer Science  
We advocate that dropping the constraints imposed in [8] leads to a more general and elegant theory that includes parity and mean payoff games as particular limit cases.  ...  Shapley [16] , is also pertinent in the context of much more recent theory of stochastic parity games [7,6,5] which were proposed as a tool for verification of probabilistic systems.  ...  In perfect information stochastic games the set S of states is partitioned onto the sets S 0 and S 1 of states of player 0 and player 1 respectively.  ... 
doi:10.1016/j.entcs.2004.07.005 fatcat:n3fidaohvjdytlejslu3urhxte

Blackwell-Optimal Strategies in Priority Mean-Payoff Games

Hugo Gimbert, Wiesław Zielonka
2010 Electronic Proceedings in Theoretical Computer Science  
We examine perfect information stochastic mean-payoff games - a class of games containing as special sub-classes the usual mean-payoff games and parity games.  ...  We show that deterministic memoryless strategies that are optimal for discounted games with state-dependent discount factors close to 1 are optimal for priority mean-payoff games establishing a strong  ...  The connections between discounted and mean-payoff games become much tighter when we consider perfect information stochastic games (games where players play in turns).  ... 
doi:10.4204/eptcs.25.5 fatcat:oyrh4dh5ajegxhgofrhvlltc34

BLACKWELL OPTIMAL STRATEGIES IN PRIORITY MEAN-PAYOFF GAMES

HUGO GIMBERT, WIESŁAW ZIELONKA
2012 International Journal of Foundations of Computer Science  
We examine perfect information stochastic mean-payoff games -a class of games containing as special sub-classes the usual mean-payoff games and parity games.  ...  We show that deterministic memoryless strategies that are optimal for discounted games with state-dependent discount factors close to 1 are optimal for priority mean-payoff games establishing a strong  ...  The connections between discounted and mean-payoff games become much tighter when we consider perfect information stochastic games (games where players play in turns).  ... 
doi:10.1142/s0129054112400345 fatcat:3kwfnksbzrcglpjevc4yf77jde

Pure and Stationary Optimal Strategies in Perfect-Information Stochastic Games with Global Preferences [article]

Hugo Gimbert
2016 arXiv   pre-print
We examine the problem of the existence of optimal deterministic stationary strategiesintwo-players antagonistic (zero-sum) perfect information stochastic games with finitely many states and actions.We  ...  ' preferences are not expressed by payoffs.  ...  cases of deterministic games and of perfect-information stochastic games.  ... 
arXiv:1611.08487v1 fatcat:isk4ney4ercebp74vgh7uvbwpq

Nearest Fixed Points and Concurrent Priority Games [chapter]

Bruno Karelovic, Wiesław Zielonka
2015 Lecture Notes in Computer Science  
As it is known the values of different states in parity games (deterministic parity games, or stochastic perfect information parity games or concurrent parity games) can be expressed by formulas of µ-calculusa  ...  In this paper we examine concurrent priority games that generalize parity games and we relate the value of such games to a new form of fixed point calculus -the nearest fixed point calculus.  ...  Perfect information stochastic priority games also admit optimal memoryless strategies, however we do not know if they can be reduced to parity games.  ... 
doi:10.1007/978-3-319-22177-9_29 fatcat:7ddnvs2svna3ri3s6rpiese42q

Playing in stochastic environment: from multi-armed bandits to two-player games

Wieslaw Zielonka, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
It turns out that under some general conditions the problem for twoplayer games can be reduced to the same problem for one-player games which in turn can be reduced to a simpler related problem for multi-armed  ...  Given a zero-sum infinite game we examine the question if players have optimal memoryless deterministic strategies.  ...  Note also that a lifting of a mean-payoff game is again a mean-payoff game, similarly a lifting of a parity game is a parity game, and a lifting of a priority mean-payoff game is a priority mean-payoff  ... 
doi:10.4230/lipics.fsttcs.2010.65 dblp:conf/fsttcs/Zielonka10 fatcat:kwcsmza5grfafnd3eoqeuqvlhu

When Can You Play Positionally? [chapter]

Hugo Gimbert, Wiesław Zielonka
2004 Lecture Notes in Computer Science  
To verify the robustness of our conditions we show that all popular payoff mappings, such as mean payoff, discounted, parity as well as several other payoffs satisfy them. ⋆  ...  We consider infinite antagonistic games over finite graphs. We present conditions that, whenever satisfied by the payoff mapping, assure for both players positional (memoryless) optimal strategies.  ...  An intriguing open question is whether our three conditions assure the existence of optimal positional pure strategies for perfect information stochastic games.  ... 
doi:10.1007/978-3-540-28629-5_53 fatcat:okwltbtyoncbrhvdju5vcmo7jq

Limits of Multi-Discounted Markov Decision Processes

Hugo Gimbert, Wieslaw Zielonka
2007 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)  
We introduce a new class of payoff functions called the priority weighted payoff functions, which are generalization of both parity and mean-payoff functions.  ...  For example a mean-payoff function evaluates average performance, whereas a discounted payoff function gives more weights to earlier performance by means of a discount factor.  ...  The special case of perfect information games (turn-based games) is easy, this is ongoing work which will be published soon.  ... 
doi:10.1109/lics.2007.28 dblp:conf/lics/GimbertZ07 fatcat:7i3aoegw6bd4hkz7rg4n3b2yya

Generic uniqueness of the bias vector of finite stochastic games with perfect information [article]

Marianne Akian, Stéphane Gaubert, Antoine Hochart
2017 arXiv   pre-print
Mean-payoff zero-sum stochastic games can be studied by means of a nonlinear spectral problem.  ...  In this paper, we consider perfect-information zero-sum stochastic games with finite state and action spaces, thinking of the transition payments as variable parameters, transition probabilities being  ...  Preliminaries on zero-sum stochastic games 2.1. Games with perfect information.  ... 
arXiv:1610.09651v2 fatcat:7k6y4ekeobhefhfi3xxn7ifc4u

Existential Theory of the Reals Completeness of Stationary Nash Equilibria in Perfect Information Stochastic Games [article]

Kristoffer Arnsfelt Hansen, Steffan Christ Sølvsten
2020 arXiv   pre-print
We show that the problem of deciding whether in a multi-player perfect information recursive game (i.e. a stochastic game with terminal rewards) there exists a stationary Nash equilibrium ensuring each  ...  player a certain payoff is Existential Theory of the Reals complete.  ...  Conclusion In this paper we have focused on the complexity of decision problems concerning stationary NE in perfect information stochastic games, and we have obtained the first ∃R-completeness result for  ... 
arXiv:2006.08314v2 fatcat:sn6r5552ezfxtfe4m76tnoyska

Perfect-Information Stochastic Games with Generalized Mean-Payoff Objectives [article]

Krishnendu Chatterjee, Laurent Doyen
2016 arXiv   pre-print
In the synthesis of stochastic reactive processes, the traditional model is perfect-information stochastic games, where some transitions of the game graph are controlled by two adversarial players, and  ...  We consider such games where the objective is the conjunction of several quantitative objectives (specified as mean-payoff conditions), which we refer to as generalized mean-payoff objectives.  ...  Perfect-information stochastic games.  ... 
arXiv:1604.06376v1 fatcat:orzcxxl2vnbtze7jok5rhxzfsu

A Survey of Bidding Games on Graphs (Invited Paper)

Guy Avni, Thomas A. Henzinger, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game.  ...  Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly.  ...  Definition 19 (Mean-payoff value in random-turn games). For p ∈ [0, 1], since G is a mean-payoff game, the random-turn game RT(G, p) is a stochastic mean-payoff game.  ... 
doi:10.4230/lipics.concur.2020.2 dblp:conf/concur/AvniH20 fatcat:ngem4jljbfey5hg24lpsi54fsq

∃ℝ-Completeness of Stationary Nash Equilibria in Perfect Information Stochastic Games

Kristoffer Arnsfelt Hansen, Steffan Christ Sølvsten, Daniel Kráľ, Javier Esparza
2020 International Symposium on Mathematical Foundations of Computer Science  
We show that the problem of deciding whether in a multi-player perfect information recursive game (i.e. a stochastic game with terminal rewards) there exists a stationary Nash equilibrium ensuring each  ...  player a certain payoff is ∃ℝ-complete.  ...  Perfect Information Stochastic Games An m-player perfect information stochastic game G is given by a directed graph (digraph) D = (V, A).  ... 
doi:10.4230/lipics.mfcs.2020.45 dblp:conf/mfcs/HansenS20 fatcat:i5zcoyys5fgrlgacz7hdogx2yu

On the computational complexity of solving stochastic mean-payoff games [article]

Vladimir Gurvich, Peter Bro Miltersen
2008 arXiv   pre-print
We consider some well-known families of two-player, zero-sum, perfect information games that can be viewed as special cases of Shapley's stochastic games.  ...  mean-payoff games with rewards and probabilities given in binary.  ...  Introduction We consider some well known families of two-player, zero-sum, turn-based, perfect information games that can be viewed as specical cases of Shapley's stochastic games [12] .  ... 
arXiv:0812.0486v1 fatcat:f7h44jvya5ae3lzuxfsdniqqmi
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