Structure in the Value Function of Two-Player Zero-Sum Games of Incomplete Information

In this paper, we introduce a new formulation for the value function of a zero-sum Partially Observable Stochastic Game (zs-POSG) in terms of a `plan-time sufficient statistic', a distribution over joint sets of information. We prove that this value function exhibits concavity and convexity with respect to appropriately chosen subspaces of the statistic space. We anticipate that this result is a key pre-cursor for developing solution methods that exploit such structure. Finally, we show that the formulation allow us to reduce a finite zs-POSG to a `centralized' model with shared observations, thereby transferring results for the latter (narrower) class of games to games with individual observations