On stochastic incentive control problems with partial dynamic information
type: Item
instance of: scholarly article
title: On stochastic incentive control problems with partial dynamic information
zbMATH Open document ID: 0568.93057
DOI: 10.1016/0167-6911(85)90057-X
author: Derya H. Cansever
author: Tamer Başar
published in: Systems \& Control Letters
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 91A60
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 93A13
Mathematics Subject Classification ID: 90B50
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 3908296
zbMATH Keywords: multiperson decision making
zbMATH Keywords: stochastic information
zbMATH Keywords: incentive problem
zbMATH Keywords: leader
zbMATH Keywords: follower
reviewed by: Geert Jan Olsder
MaRDI profile type: Publication
cites work: Performance bounds for hierarchical systems under partial dynamic information
cites work: Affine Incentive Schemes for Stochastic Systems with Dynamic Information
cites work: Optimum/near-optimum incentive policies for stochastic decision problems involving parametric uncertainty
cites work: Incentive problems: A class of stochastic Stackelberg closed-loop dynamic games
cites work: Optimal and near-optimal incentive strategies in the hierarchical control of Markov chains
full work available at URL: 0167-6911(85)90057-x
OpenAlex ID: W2174047771
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description: scientific article; zbMATH DE number 3908296