Two-player Non-zero-sum Games: a Reduction
نویسنده
چکیده
In this chapter, we focus on finite two-player non-zero-sum stochastic games. Following the notations used in earlier chapters, we let S be the state space, and A and B be the action sets of players 1 and 2 respectively. All three sets S,A and B are finite. Generic elements of S, A and B will be denoted by z, a and b. We let p(·|z, a, b) be the transition function of the game and r : S × A× B → R2 be the (stage) payoff function of the game. We deal with games with complete information, perfect recall and perfect monitoring. Thus, at each stage n ≥ 0, the two players know the play hn = (z1, a1, b1, ..., zn) up to that stage, and simultaneously choose actions an and bn. The next state zn+1 is drawn according to p(·|zn, an, bn) and the play proceeds to the next stage. The goal of this chapter, together with the next one, is to give an overview of the proof of Theorem 1.
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