Accession Number : AD0783698

Title :   Fleming's Randomized Game and His Parabolic Partial Differential Equation,


Personal Author(s) : Danskin,John M.

Report Date : APR 1974

Pagination or Media Count : 156

Abstract : Proceeding from first principles and making no use of existing partial differential equations (PDE) theory, the paper gives a direct and elementary proof that the value of Wendell Fleming's 1964 randomized mixed-strategy game exists and satisfies his parabolic PDE. Fleming required the terminal function to have Lipschitzian first and second partial derivatives; this paper requires only that the terminal function and its gradient be Lipschitzian. The solution is given a new representation, which allows precise Lipschitz and Holder estimates to be made. A trick of Fleming allows the deduction of a uniqueness and existence theorem for a class of parabolic equations with Laplacian operator under the lightened terminal conditions. (Author)

Descriptors :   *Game theory, *Partial differential equations, Strategy, Inequalities, Potential theory, Theorems

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE