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Gambling in a Malthusian Universe

A Game-Theoretic approach to the Paradoxes of Expected Utility

GREGORY B. POLLOCK

Northwestern University and Arizona State University

KEITH A. LEWIS

Metropolitan Life

Prospect choice is generally viewed as a game against nature. This article models prospect choice as an n-person game where each subject assumes that n-1 others will be exposed to the same decision problem (prospect choice set) as self; the goal is not to "beat nature" but to do relatively better than rivals exposed to the same problem. Preference becomes strategy choice in n-person Nash equilibrium. When symmetric pure strategy equilibria do not exist, choice is a symmetric randomized equilibrium; here, uncertainty (probabilistic response) becomes a method of dealing with uncertainty in nature. The approach produces, qualitatively, several empirical expected utility paradoxes (the certainty effect, intransitive cycles, and one form of reflection), and an evolutionary game-theoretic extension accounts for all the phenomena revealed by the research of Kahneman and Tversky.

Rationality and Society, Vol. 5, No. 1, 85-106 (1993)
DOI: 10.1177/1043463193005001008
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K. H. Schlag and G. B. Pollock
SOCIAL ROLES AS AN EFFECTIVE LEARNING MECHANISM
Rationality and Society, November 1, 1999; 11(4): 371 - 397.
[Abstract] [PDF]