Hybrid strategy in multiperiod mean-variance framework

In multiperiod mean-variance framework, the investor suffers time inconsistency. Current solution schemes either reformulate the problem into a sequential by assuming there is no ability of conducting self-control, or reformulate the problem into a planner-doer game by assuming there is enough ability of conducting self-control. However, in reality, the investor often has limited ability of conducting self-control and we reformulate the problem as a planner-middleman-doer game. We derive the explicit expression of the equilibrium strategy.