A Nash Equilibrium for Differential Games with Moving-Horizon Strategies

Our paper aims at introducing a moving-horizon interaction in a strategic context. We assume that, in each instant of time, players can predict the effects of their actions and those of their opponents on a finite moving horizon. We define an equilibrium concept, which is consistent in this setting, and develop an appropriate algorithm to compute it by using nonlinear model predictive control techniques. Focusing on the length of forecasting horizon, we propose two economic interpretations for our equilibrium, based on the limited rationality and political economy literature: a simple 2 players’ nonlinear policy game, and what happens to debt stabilization when policymakers have different values of the forecasting horizon. To provide some practical insights of our approach, we consider a debt stabilization game in a monetary union. We consider three players; two nonlinear differential constraints; and assume that one player controls one instrument which is not additive but has some multiplicative effects on the state variables.