On Games of Survival
ResearchPublished 1956
In a game of survival, two players with limited resources play a zero-sum game repeatedly until one of them is ruined. The solution of the survival game gives one a measure of the value of resources in terms of survival probabilities. In this paper the zero-sum game is expressed as a finite matrix, but with (possibly) incommensurable entries; hence the number of different distributions of resources that can occur during a single play may be infinite. The existence of a value and optimal strategies is proved, using the theory of semi-martingales. A simple approximation to the solution is described, and several examples are discussed.
Topics
Document Details
- Copyright: RAND Corporation
- Availability: Available
- Year: 1956
- Print Format: Paperback
- Paperback Pages: 47
- Paperback Price: $23.00
- DOI: https://doi.org/10.7249/P622
- Document Number: P-622
Citation
RAND Style Manual
Chicago Manual of Style
Milnor, John Willard and Lloyd S. Shapley, On Games of Survival, RAND Corporation, P-622, 1956. As of September 12, 2024: https://www.rand.org/pubs/papers/P622.html
Milnor, John Willard and Lloyd S. Shapley, On Games of Survival. Santa Monica, CA: RAND Corporation, 1956. https://www.rand.org/pubs/papers/P622.html. Also available in print form.
This publication is part of the RAND paper series. The paper series was a product of RAND 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.
This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.
RAND 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.