A note on polynomial and separable games.

by David Gale, Oliver Alfred Gross

Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback16 pages $15.00 $12.00 20% Web Discount

A proof that given a pair of infinite metric spaces and a pair of respective finite mixed strategies on them, a separable game exists 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, corresponding to any given finite mixture, a symmetric polynomial-like game can be obtained with bounded (skew-symmetric) continuous payoff so that the given strategy is the only optimal one. If the spaces are bounded subspaces of Euclidean n-space with sufficiently many cluster points in their closures, the payoff can be a polynomial and have the desired property.

This report is part of the RAND Corporation Paper series. The paper was a product of the RAND Corporation from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/principles.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.