Stochastic Stackelberg games: Nonnested multistage multiagent incentive problems

Abstract

Recent progress in Stackelberg dynamic games concentrates on either the deterministic situations or partially nested stochastic problems. In this paper, a class of nonnested' stochastic Stackelberg dynamic games, namely LOG additive incentive problems, is solved. By explicitly introducing two essential ideas-matching answers and GPD phenomenon, each incentive problem can be converted into a set of decoupled inverse team problems (ITP's). The solution of each ITP can then be found by solving a set of linear algebraic equations if it exists. Moreover, it is shown that, for a wide class of problems, if there exist more agents, then it is more advantageous to the leader in the sense that he has more free parameters to manipulate. Therefore, the leader can always induce the agents' cooperation as a team by means of incentives if there are enough agents. Application to a class of stochastic closed-loop dynamic Stackelberg games is also given. Since typically there exist a large number of free parameters in our solution, adequate parameters can then be chosen to make the incentive scheme satisfy additional useful properties such as balanced budget and noise robustness. These topics are treated in the Appendices.