A VARIATIONAL APPROACH TO DIFFERENTIAL GAMES
Abstract
A class of differential games having pure strategy solutions is investigated by means of results and techniques from the calculus of variations. These games are related to two Bolza problems with differential inequalities as added side constraints. Necessary conditions that must hold along an optimal path are derived from the theory of the related Bolza problems. These conditions are (1) a multiplier rule, together with transversality conditions and jump conditions, (2) a local min-max condition that is related to the Weierstrass condition, and (3) an analogue of the Clebsch condition. The continuity and differentiability pp yty properties of the value of the game are derived. It is shown that, wherever the value is differentiable, it satisfies an analogue of the Hamilton-Jacobi equation. Sufficient conditions are given in terms of the notion of a field and of a local min-max condition. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 30, 1961
- Accession Number
- AD0260560
Entities
People
- L.d. Berkovitz
Organizations
- RAND Corporation