Absolutely cooperative solution for a linear,multiplayer differential game

If the players of ann-player differential game agree to cooperate, then the solutions to the game should be confined to undominated ones. A property of an undominated or Pareto-optimal solution is that, when compared locally with any other solution, at least one player must do worse or all do the same if they use a solution other than the Pareto-optimal one.Closely related to the concept of a Pareto-optimal solution is the concept of an absolutely cooperative solution. The absolutely cooperative solution is given the property that, when compared locally with any other solution, every player will do no better if a solution other than the absolutely cooperative one is used.A set of necessary and sufficient conditions for an absolutely cooperative solution is presented in this paper. The circumstance under which the control variables may take on interior values is also included.This research was supported in part by NASA Grant No. NGR-03-002-011.