Abstract
AbstractThis chapter discusses Pareto optimality in infinite horizon cooperative difference games. Under an assumption about the Lagrange multipliers, necessary conditions for the existence of Pareto solutions are put forward. Furthermore, two conditions are introduced to ensure that the assumption on the Lagrange multipliers is set up. In addition, it is shown that necessary conditions are also sufficient under a convexity assumption and a transversality condition. Next, the LQ case is studied. By the discussion of the convexity of the cost functionals, the characterization of Pareto solutions is explored. If the system is stabilizable, then the solvability of the related ARE provides a sufficient condition under which all Pareto solutions can be obtained based on the solutions of an introduced ALE.
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