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Perfect-Information Stochastic Mean-Payoff Parity Games
[chapter]
2014
Lecture Notes in Computer Science
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, 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?
2005
Electronical Notes in Theoretical Computer Science
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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
2010
Electronic Proceedings in Theoretical Computer Science
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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
2012
International Journal of Foundations of Computer Science
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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]
2016
arXiv
pre-print
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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]
2015
Lecture Notes in Computer Science
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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
2010
Foundations of Software Technology and Theoretical Computer Science
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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]
2004
Lecture Notes in Computer Science
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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
2007
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
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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]
2017
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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]
2016
arXiv
pre-print
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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)
2020
International Conference on Concurrency Theory
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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
2020
International Symposium on Mathematical Foundations of Computer Science
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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]
2008
arXiv
pre-print
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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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