Characterizing Properties of the Value Function for Stochastic Games

摘要

The axiomatic characterization of the value function of two-person zero-sum games in normal form is extended to dynamic games. Special attention is given to the value function of discounted two-person zero-sum stochastic games. Furthermore, value functions for stochastic games with arbitrary evaluation rules and general state as well as action spaces are examined. The characterizing axioms are indicated by the terms objectivity, monotony, and sufficiency (or symmetry) for both players. The concept of a superfluous action is used for a player in a state of the game. Such an action can be ignored by a player without his being punished, since the value of the game remains invariant. It is also shown that the characterizing axioms are mutually independent.