A NOTE ON POLYNOMIAL AND SEPARABLE GAMES
Abstract
It is shown that, given a pair of infinite metric spaces and a pair of respective finite mixed strategies on them, there exists a separable game with bounded continuous payoff on their cartesian product such that the given strategies constitute the unique solution of the game. If the spaces are identical, then, corresponding to any given finite mixture, one can find a symmetric polynomial-like game with bounded (skew-symmetric) continuous payoff such that the given strategy is the only optimal one. A stronger conclusion holds if the spaces are bounded sub spaces of Euclidean n-space with sufficiently many cluster points in their closures, in that the payoff can be a polynomial and have the desired property.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 14, 1957
- Accession Number
- AD0606592
Entities
People
- David Gale
- Oliver Gross
Organizations
- RAND Corporation