Learning in multilevel games with incomplete information. II

Multilevel games are abstractions of situations where decision makers are distributed in a network environment. In Part I of this paper, the authors present several of the challenging problems that arise in the analysis of multilevel games. In this paper a specific set up is considered where the two games being played are zero-sum games and where the decision makers use the linear reward-inaction algorithm of stochastic learning automata. It is shown that the effective game matrix is decided by the willingness and the ability to cooperate and is a convex combination of two zero-sum game matrices. Analysis of the properties of this effective game matrix and the convergence of the decision process shows that players tend toward noncooperation in these specific environments. Simulation results illustrate this noncooperative behavior.