On stochastic incentive control problems with partial dynamic information
During the last five years there has been a considerable activity in control theoretic descriptions of economic incentive problems. Initially deterministic problems were considered and then various stochastic extensions were studied. The current paper fits within this framework. The convential incentive problem deals with the case in which the leader knows the actions of the follower(s) in order to determine his own action. Ahead of time the leader announces his strategy as a function of the followers' actions and as a result of this and the followers' decisions, the leader's decision is fixed. The contribution of this paper is an investigation of what the leader can achieve if now only a linar combination of the followers' actions is known (instead of the individual actions). Conditions are given for which the lower bound which the leader can achieve for his cost function in case he only knows this linear combination of the followers' actions equals the lower bound (which also can be achieved) if the individual actions are known to the leader. This lower bound equals the team minimum of the leader's cost function. The stochastic aspect of the decision process lies in the fact that the followers have only noise mearurements and these individual noise measurements are also known to the leader. The results mentioned above have been proved for the case of finite probability spaces and the authors state that infinite probability spaces offer new challenges. It is a theoretical contribution in which the role of information (who knows what when) is crucial. No applications are given or hinted at.
scientific article; zbMATH DE number 3908296