- EconomicsProceedings of the National Academy of Sciences
The historical context and the impact of Shapley’s contribution to stochastic games, which were the first general dynamic model of a game to be defined, are summarized.
Stochastic games: Existence of the MinMax
- Mathematics, Economics
The existence of the value for stochastic games with finitely many states and actions, as well as for a class of stochastic games with infinitely many states and actions, is proved in . Here we…
Sensitive equilibria for ergodic stochastic games with countable state spaces
- MathematicsMath. Methods Oper. Res.
The main results in this paper concern the existence of sensitive optimal strategies in some classes of zero-sum stochastic games with denumerable state spaces and the provision of a new Nash equilibrium theorem for a class of ergodic nonzero-sum StochasticGames with den enumerated state spaces.
Weighted-average stochastic games with constant payoff
- EconomicsOper. Res.
In a zero-sum stochastic game, at each stage, two opponents make decisions which determine a stage reward and the law of the state of nature at the next stage, and the aim of the players is to…
Uniform value for recursive games with compact action sets
- MathematicsOper. Res. Lett.
A Stay-in-a-Set Game without a Stationary Equilibrium
We give an example of a finite-state two-player turn-based stochastic game with safety objectives for both players which has no stationary Nash equilibrium. This answers an open question of Secchi…
Communicating zero-sum product stochastic games
- MathematicsJournal of Mathematical Analysis and Applications
Stopping games with randomized strategies
Abstract. We study stopping games in the setup of Neveu. We prove the existence of a uniform value (in a sense defined below), by allowing the players to use randomized strategies. In constrast with…
Total Reward Stochastic Games and Sensitive Average Reward Strategies
- Computer Science
In this paper, total reward stochastic games are surveyed and it is shown that total reward games with finite state space are strategically equivalent to a class of average Reward games with an infinite countable state space.
Computing Stationary Nash Equilibria of Undiscounted Single-Controller Stochastic Games
- EconomicsMath. Oper. Res.
Given a two-person, nonzero-sum stochastic game where the second player controls the transitions, we formulate a linear complementarity problem LCP( q, M) whose solution gives a Nash equilibrium pair…