Pareto efficient cheating in dynamic reversed Stackelberg games: the open loop linear quadratic case

摘要

In a Dynamic Reversed Stackelberg game, the leader can typically improve his payoff by cheating, that is, by announcing a strategy that he will not follow. However, as shown by Vallee, Deissenberg, and Basar in a recent paper, it is possible that some of the cheating strategies that are beneficial for the leader also improve the payoff of the follower, while others deteriorate it. In this paper, we introduce the concept of a Pareto Beneficial Cheating strategy, that is, of a cheating strategy that leads to a Pareto efficient outcome and improves the situation of both the leader and the follower compared to the solution without cheating. We derive the open-loop Cheating Strategy for an extended standard discrete time linear-quadratic Dynamic Reversed Stackelberg game allowing for the follower being cheating adverse. Numerical illustrations are given.