NONZERO-SUM DIFFERENTIAL GAMES: CONCEPTS AND MODELS.
Abstract
A general class of differential games, where the N players try to minimize different cost criteria by controlling inputs to a single dynamic system, is investigated as an extension of optimal control theory. Dropping the usual zero-sum assumption makes it possible to model a more realistic class of competitive situations where mutual interest is important. The nonzero-sum formulation has several interesting analytic and conceptual features not found in zero-sum differential games. It is no longer obvious what should be demanded of a 'solution,' and three types of solution concepts are discussed: Nash equilibrium, minimax, and noninferior (or Pareto optimal) strategies. For one special case, the 'linear-quadratic' differential game, all of these solutions can be computed exactly by solving sets of coupled ordinary matrix differential equations. Some simple examples are solved, and series of more difficult but more realistic nonzero-sum differential game situations are presented (but not solved) for models of economic oligopoly, advertising policy, labor-management negotiations, and international trade. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1969
- Accession Number
- AD0694973
Entities
People
- Alan W. Starr
Organizations
- Harvard University