Repeated games with incomplete information and transportation problems
The authors are considering stochastic games whose payoff matrix \(A^s\) depends on a state of nature \(s\) chosen by a chance move according to a probability measure \(\mathbf{p}\). In particular, they look at games \(\Gamma_n(A^s,\mathbf{p})\) in which (a) player 1 knows the state of nature before the game starts and player 2 only know the probability measure \(\mathbf{p}\) (lack of information on one side), and (b) the payoff matrix is separable, i.e., the entries are of the form \(a_{ij}^s = a_{ij} + b_i^s\). Games like this have been considered by Aumann, Maschler, Mertens and Zamir, and \textit{V. Domansky} and \textit{V. Kreps} [Int. J. Game Theory 23, No. 2, 89-99 (1994; Zbl 0803.90143)]. The authors connect the values of these games to the multinomial transportation problem by showing that the value of the game \(\Gamma_n(A^s,\mathbf{p})\) is equal to the optimal solution of the multinomial transportation problem.
scientific article; zbMATH DE number 1439900