Characterizing properties of the value function of stochastic games
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In the present note, the axiomatic characterization of the value function of two-person, zero-sum games in normal form by Vilkas and Tijs is extended to the value function of discounted, two-person, zero-sum stochastic games. The characterizing axioms can be indicated by the following terms: objectivity, monotony, and sufficiency for both players; or sufficiency for one of the players and symmetry. Also, a characterization without using the monotony axiom is given.
[1] E. I. Vilkas. Axiomatic Definition of the Value of a Matrix Game , 1963 .
[2] L. Shapley,et al. Stochastic Games* , 1953, Proceedings of the National Academy of Sciences.
[3] S. H. Tijs. A characterization of the value of zero-sum two person games , 1981 .