Cooperative dynamic game, discrete time case

Abstract

In this paper, we study the cooperative dynamic game problem for discrete time case. We solved this problem by determining Pareto solution, continued by finding Nash-bargaining solution. We assume the difference equation in this problem is linear and time invariant. The objective function for each player has the quadratic form and positive definite. We can proof that Pareto solution can be determined by minimizing linear convex combination of all objective functions. The disagreement point of all players is obtained by finding minimax point. The Nash-bargaining solution is selecting a point in Pareto frontier such that the product of utility gains from disagreement point is maximal.