Repeated games and multinomial distributions

Abstract

We consider two person zero-sum games with lack of information on one side given bym matrices of dimensionm×m. We suppose the matrices to have the following “symmetric” structure:a ij s =a ij +cδ i s ,c>0, whereδ i s =1 ifi=s andδ i s =0 otherwise. Under certain additional assumptions we give the explicit solution for finite repetitions of these games. These solutions are expressed in terms of multinomial distributions. We give the probabilisitc arguments which explain the obtained form of solutions. Applying the Central Limit Theorem we get the description of limiting behavior of value closely connected with the recent results of De Meyer [1989], [1993].