Optimal strategies in cooperative games with terminal payoff

This paper presents two developments in dynamic game theory. The first contribution is for Pareto optimal, finite-time, nonlinear game subject to hard terminal constraints. The two-player problem is formulated as a time-dependent Hamilton-Jacobi-Isaacs (HJI) equation and a series solution methodology is applied to obtain the optimal feedback solution. Several numerical examples are included and we develop the Pareto frontier for the general quadratic payoff function with a nonlinear co-operation model and terminal constraints. The second development involves a structured cooperation approach among players by the introduction a linear cooperation equation. The devised methodology is explored for multiplayer linear quadratic differential games. In order to focus the new theoretical development, some simple, but concept-based numerical and analytical solutions are discussed to illustrate the desired benefits in each player's payoff function.

Optimal strategies in cooperative games with terminal payoff Conference Paper