Even Risk-Averters may Love Risk

Theory and Decision 52 (1):81-99 (2002)

Abstract
A decision maker bets on the outcomes of a sequence of coin-tossings. At the beginning of the game the decision maker can choose one of two coins to play the game. This initial choice is irreversible. The coins can be biased and the player is uncertain about the nature of one (or possibly both) coin(s). If the player is an expected-utility maximizer, her choice of the coin will depend on different elements: the nature of the game (namely, whether she can observe the outcomes of the previous tosses before making her next decision), her utility function, the prior distribution on the bias of the coin. We will show that even a risk averter might optimally choose a riskier coin when learning is allowed. We will express most of our results in the language of stochastic orderings, allowing comparisons that are valid for large classes of utility functions
Keywords Coin tossing  Exchangeable random variables  Games of chance  Learning  Risk Aversion  Stochastic comparison
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DOI 10.1023/A:1015513000587
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