L.S. Shapley. Stochastic games. Proc. National Academy of Sciences, 39:1095--1100, 1953.  Home/Search   Document Not in Database   Summary   Related Articles   Check

..... In this section, we present, to our knowledge, the first result on the existence of a purestrategy equilibrium. A multi stage game is typically represented as a stochastic (Markov) game, where there is an underlying set of states, and the game shifts between these states from stage to stage [3, 20, 21] . At every stage, each player s payoff depends not only on the players actions, but also on the state. Furthermore, the probability of transitioning to a given state is determined by the current state and the players current actions. Hardness results for such games cannot be obtained simply by ....

Lloyd S Shapley. Stochastic games. Proc. of the National Academy of Sciences, 39:1095--1100, 1953.

....In this section, we present, to our knowledge, the first result on the existence of a pure strategy equilibrium. A multi stage game is typically represented as a stochastic (Markov) game, where there is an underlying set of states, and the game shifts between these states from stage to stage [12, 45, 46]. At every stage, each player s payoff depends not only on the players actions, but also on the state. Furthermore, the probability of transitioning to a given state is determined by the current state and the players current actions. Hardness results for such games cannot be obtained simply by ....

Lloyd S Shapley. Stochastic games. Proc. of the National Academy of Sciences, 39:1095--1100, 1953.

....dynamic environment. With major application areas in economic analysis and operations research, there has been much recent interest in stochastic game models in the context of Arti cial Intelligence and machine learning (e.g. BT95, Pat97, Ras94, Lit94] Starting from the seminal paper of Shapley [Sha53], there have been an extensive and continuing research on the theory of stochastic games, focusing on the existence of the value, optimal strategies, and their computation; see [FV96] for a recent review. Game theory has focused on the analysis of con icts between rational agents, who make ....

L. Shapley. Stochastic games. Proc. of National Academy of Science, Math., pages 1095-1100, 1953.

....horizon problem with a discount rate of 0:9 has e V (s 1 ) 29:9, while for a finite horizon problem, e V t (s 1 ) is given by 10b t 1 3 c. MMDPs, while a natural extension of MDPs to cooperative multiagent settings, can also be viewed as a type of stochastic game as formulated by Shapley [14]. Stochastic games were originally formulated for zero sum games only (and as we will see, the zero sum assumption alleviates certain difficulties) whereas we focus on the (equally special) case of cooperative games. 3 Coordination Problems and Coordination Mechanisms The example MMDP above has ....

.... computation of value in this case is an understanding of the coordination mechanism used to (stochastically) select joint actions in the presence of multiple equilibria, and the ability to associate a value with any state of the MMDP (given the state of the mechanism) Shapley s stochastic games [14] provide a related sequential multiagent decision model with a a well defined value for game states. This value, however, is a consequence of the zero sum assumption, which removes the reliance of state value on the selection of a (stage game) equilibrium. In particular, it does not apply to fully ....

L. S. Shapley. Stochastic games. Proc. National Academy of Sciences, 39:327--332, 1953.

....of consistency, we use the term mentor to describe any agent from which an observer can learn, even if the mentor is an unwilling participant. 2 This is not to say that the other mentors cannot be learners or even imitators themselves. 3 MMDPs could be viewed as a form of stochastic game [20]; since Shapley s original formulation involved the zero zum assumption, we use different terminology to avoid confusion. of actions, Pr i (tjs; a) the stochastic state transition function and R i (s) its reward function (defined over S i ) For instance, in a grid world, we might assume that the ....

L. S. Shapley. Stochastic games. Proc. National Academy of Sciences, 39:327--332, 1953.

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L.S. Shapley. Stochastic games. Proc. National Academy of Sciences, 39:1095--1100, 1953.

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