ON DIFFERENTIAL GAMES WITH SURVIVAL PAYOFFS
Abstract
A class of survival games is considered in an arbitrary n-dimensional region R, and with an arbitrary payoff function f(x) on the boundary. If the steps are uniformly decreased in size, the equations specifying the changes in the state of the game tend to approximate the equations of a differential game. A particular class of games is treated in which neither player can force the state of the game to proceed in any direction. It is shown that under certain conditions, the upper and lower values of the approximating games actually converge to the same function. The limiting value is given by the solution of L(V) = O, with boundary value f(x), where L(V) is a certain second-order differential operator associated with the game.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 22, 1955
- Accession Number
- AD0604950
Entities
People
- Herbert Scarf
Organizations
- RAND Corporation