Existence of $p$-equilibrium and optimal stationary strategies in stochastic games

Himmelberg, C. J.; Parthasarathy, T.; Raghavan, T. E. S.; Vleck, F. S. Van

doi:10.1090/s0002-9939-1976-0418931-1

“…It may however depend on > 0 and this dependence may be necessary, as shown by examples of Everett. In contrast, it is known that Player II has an exact optimal strategy that is guaranteed to achieve the value of the game, without any additive error [17,13].…”

Section: M}mentioning

confidence: 99%

The Complexity of Solving Reachability Games Using Value and Strategy Iteration

Hansen

¹

,

Ibsen-Jensen

²

,

Miltersen

³

2011

Computer Science – Theory and Applications

View full text Add to dashboard Cite

Two standard algorithms for approximately solving two-player zerosum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2 m Θ(N ) on the worst case number of iterations needed by both of these algorithms for providing non-trivial approximations to the value of a game with N non-terminal positions and m actions for each player in each position. In particular, both algorithms have doubly-exponential complexity. Even when the game given as input has only one non-terminal position, we prove an exponential lower bound on the worst case number of iterations needed to provide non-trivial approximations.

show abstract

“…The second stop is according to ς * given by (19) for Player 2 and δ * given by (20) for Player 1. The value function of the problem is given by (21), the expected value with respect to P (r,lr) of AMC by (22) and its limit by (23).…”

Section: The Best Vs the Best Or The Second Best Gamementioning

confidence: 99%

Non-Zero-Sum Stochastic Games

Jaśkiewicz¹,

Nowak²

2017

Handbook of Dynamic Game Theory

View full text Add to dashboard Cite

Abstract. This paper treats stochastic games. A nonzero-sum average payoff stochastic games with arbitrary state spaces and the stopping games are considered. Such models of games very well fit in some studies in economic theory and operations research. A correlation of strategies of the players, involving "public signals", is allowed in the nonzero-sum average payoff stochastic games. The main result is an extension of the correlated equilibrium theorem proved recently by Nowak and Raghavan for dynamic games with discounting to the average payoff stochastic games. The stopping games are special model of stochastic games. The version of Dynkin's game related to observation of Markov process with random priority assignment mechanism of states is presented in the paper. The zero-sum and nonzero-sum games are considered. The paper also provides a brief overview of the theory of nonzero-sum stochastic games and stopping games which are very far from being complete.

show abstract

“…The value function of the problem is given by (21), the expected value with respect to P (r,lr) of AMC by (22) and its limit by (23).…”

Section: The Best Vs the Best Or The Second Best Gamementioning

confidence: 99%

Non-Zero-Sum Stochastic Games

Jaśkiewicz¹,

Nowak²

2016

Handbook of Dynamic Game Theory

View full text Add to dashboard Cite

Abstract. This paper treats stochastic games. A nonzero-sum average payoff stochastic games with arbitrary state spaces and the stopping games are considered. Such models of games very well fit in some studies in economic theory and operations research. A correlation of strategies of the players, involving "public signals", is allowed in the nonzero-sum average payoff stochastic games. The main result is an extension of the correlated equilibrium theorem proved recently by Nowak and Raghavan for dynamic games with discounting to the average payoff stochastic games. The stopping games are special model of stochastic games. The version of Dynkin's game related to observation of Markov process with random priority assignment mechanism of states is presented in the paper. The zero-sum and nonzero-sum games are considered. The paper also provides a brief overview of the theory of nonzero-sum stochastic games and stopping games which are very far from being complete.

show abstract

Existence of $p$-equilibrium and optimal stationary strategies in stochastic games

Cited by 23 publications

References 13 publications

The Complexity of Solving Reachability Games Using Value and Strategy Iteration

The Complexity of Solving Reachability Games Using Value and Strategy Iteration

Non-Zero-Sum Stochastic Games

Non-Zero-Sum Stochastic Games

Contact Info

Product

Resources

About