Repeated games and multinomial distributions

The authors consider two person zero-sum games with lack of information on one side given by m matrices of dimension . They suppose the matrices to have the following ‘symmetric’ structure: , where if i=s and otherwise. Under certain additional assumptions the authors give the explicit solution for finite repetitions of these games. These solutions are expressed in terms of multinomial distributions. They give the probabilistic arguments which explain the obtained form of solutions. Applying the Central Limit Theorem the authors get the description of limiting behavior of value closely connected with the recent results of De Meyer.