Abstract
A stochastic game is a multi-stage game played in discrete time where, at each stage, the stage game played depends upon a parameter called state. The value of the state evolves as a function of its current value and the actions of the players. Let I be the finite set of players and S be the set of states. For each state z in S, an I-player normal form game is specified by action sets A i(z) for each player i in I and reward functions r i(z,.), i in I, from the set of action profiles at z, A (z) = Π iɛI A i(z) to the reals, ℝ. In addition, for any pair consisting of a state z in S and an action profile a in A(z), a probability p(.|z,a) on S describes the random transition.
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Sorin, S. (2003). Classification and Basic Tools. In: Neyman, A., Sorin, S. (eds) Stochastic Games and Applications. NATO Science Series, vol 570. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0189-2_3
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DOI: https://doi.org/10.1007/978-94-010-0189-2_3
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