OPTIMAL INCENTIVE STRATEGY FOR LEADER-FOLLOWER GAMES

This note gives the definition of optimal incentive strategy by which the leader suffers the least losses in punishing the follower's deviation from the decision desired by the leader. Sufficient conditions for the existence of optimal incentive strategy are given. Static and dynamic leader-follower games with quadratic cost functionals are investigated. It is shown that leader-follower games with quadratic cost functionals admit optimal incentive strategies under some conditions. For a special class of leader-follower games with the follower's decision variable being scalar, there exists a unique linear optimal incentive strategy. Such an incentive strategy can be explicitly determined.