Two Person Zero-Sum Sequential Stochastic Games with Imperfect and Incomplete Information—General Case

Abstract

In this chapter we present a unified approach to two person zero sum games with incomplete and imperfect information wherein the game matrix may not always have a sadlle point in pure strategies. This is a natural extension of the problem of Chapter 5. Under the assumption that both players A and B use the LER−P learning algorithm with the same reward and penalty parameters but the penalty parameter being very small compared to the reward parameter, it is shown that the expected mixed strategy of either player can be made, asymptotically, as close to the optimal strategy dictated by the game theory as desired, irrespective of whether or not the game matrix has a saddle point in pure strategies.