On the Existence of Easy Initial States for Undiscounted Stochastic Games

@article{Tijs1986OnTE,
  title={On the Existence of Easy Initial States for Undiscounted Stochastic Games},
  author={Stef Tijs and O. J. Vrieze},
  journal={Math. Oper. Res.},
  year={1986},
  volume={11},
  pages={506-513}
}
This paper deals with undiscounted infinite stage two-person zero-sum stochastic games with finite state and action spaces. It was recently shown that such games possess a value. But in general there are no optimal strategies. We prove that for each player there exists a nonempty set of easy initial states, i.e., starting states for which the player possesses an optimal stationary strategy. This result is proved with the aid of facts derived by Bewley and Kohlberg for the limit discount… 

Easy initial states in stochastic games

In this paper we deal with limiting average stochastic games with finite state and action spaces. For any nonzero-sum stochastic game of this type, there exists a subset of initial states for which

Solvable States in n-player Stochastic Games

  • N. Vieille
  • Economics, Mathematics
    SIAM J. Control. Optim.
  • 2000
We prove that, in every stochastic game with finitely many states and actions, there exists at least one state, starting from which an equilibrium payoff exists. This is achieved by proving that

A survey on optimality and equilibria in stochastic games

In this paper we discuss the main existence results on optimality and equilibria in two-person stochastic games with finite state and action spaces. Several examples are provided to clarify the

Stationary ɛ-optimal strategies in stochastic games

SummaryWe deal with stochastic games with finite state and action spaces for which we examine players' possibilities for playing limiting average (ɛ-)optimal by means of stationary strategies (ɛ >

Equilibrium play in matches: Binary Markov games

Stochastic games with additive transitions

References

SHOWING 1-10 OF 11 REFERENCES

An orderfield property for stochastic games when one player controls transition probabilities

When the transition probabilities of a two-person stochastic game do not depend on the actions of a fixed player at all states, the value exists in stationary strategies. Further, the data of the

On stochastic games with additive reward and transition structure

In this paper, we introduce a new class of two-person stochastic games with nice properties. For games in this class, the payoffs as well as the transitions in each state consist of a part which

Semi-markov strategies in stochastic games

It is shown, that if all players, except for one, fix a stationary strategy, then the best the remaining player can do, is solving a markov decision problem, corresponding to the fixed stationary strategies.

The Asymptotic Theory of Stochastic Games

It is proved that limn→∞{Vn/n} = limr→0rVr, where Vn is the value of the n-stage game and Vr is thevalue of the infinite- stage game with payoffs discounted at interest rate r > 0.

A finite algorithm for the switching control stochastic game

The algorithm provided provides a constructive proof of the existence of the value and of optimal stationary strategies for both players and the finiteness of the algorithm proves also the ordered field property of the switching control stochastic game.

Myopic Solutions of Markov Decision Processes and Stochastic Games

Sufficient conditions are presented for a Markov decision process to have a myopic optimum and for a stochastic game to possess a myopic equilibrium point. An optimum or an equilibrium point is said

Stochastic games with state independent transitions and separable rewards

For the class of stochastic games with separable reward functions and state independent transitions it is proved that the ordered field property holds. A solution of these stochastic games can easily

Stochastic Games*

  • L. Shapley
  • Mathematics
    Proceedings of the National Academy of Sciences
  • 1953
In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players, and the expected total gain or loss is bounded by M, which depends on N 2 + N matrices.

Linear programming and undiscounted stochastic games in which one player controls transitions

A linear programming algorithm is given and it is shown, that an optimal solution to this program corresponds to the value of the game and to optimal stationary strategies for both players.

Technical Note - Advertising Models, Stochastic Games and Myopic Strategies

Conditions that imply that the payoffs under myopic strategies are linear in the state variable are presented, which represents the number of customers for each firm, which determine a subclass of stochastic games.