Determining the Nash Equilibrium from the Reaction Relations of the Decision Makers
Abstract
Many of the problems in decision and control theory involve estimation and optimization. The theory for the identification and control of systems with several decision makers, each having different information available and each having his own performance index, is difficult. The problem of optimizing multiple objective functions has led to the development of several solution concepts. For systems in which cooperation cannot be guaranteed, a Nash solution is employed. The Nash decision strategy arises frequently in systems with multiple decision makers. An inherent property of the Nash strategy is that it prevents decision makers from cheating. When the system and cost functions are known to the decision makers, a Nash solution can be found. In Section 2 a linear quadratic game is posed and an equilibrium is proposed. In Section 3 it is shown that the proposed equilibrium is equivalent to a Nash equilibrium. It is proven in Section 4 that algorithms which are updated based upon the error in the estimated state cannot converge to a value different than the Nash equilibrium. In Section 5 an algorithm using reaction relations of the other decision makers is described. Finally, an example using the algorithm is given in Section 6.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1984
- Accession Number
- ADA161353
Entities
People
- Daniel P. Connors
Organizations
- University of Illinois Urbana–Champaign