Self-coordination in time inconsistent stochastic decision problems: A planner-doer game framework

Time inconsistency has been a thorny issue in many economic and financial decision making problems, especially when risk measures are involved in performance criteria. We develop in this paper a two-tier planner-doer game framework with self-coordination. By aligning the global interest of the planner and the local interests of the doers by applying suitable penalty functions, a degree of internal harmony (measured quantitatively by the expected cost of self-coordination) can be achieved by the self-coordination policy. We establish an axiom system for modified preferences, under which the self-coordination policy can be obtained by solving a corresponding optimization problem. We then apply our game framework successfully in dynamic mean-variance portfolio selection.