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Pre-Decision Side-Bet Sequences

Author

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  • Kim Kaleva Kaivanto
  • David Alan Peel

Abstract

Risk-averse Expected Utility (EU) decision makers with wealth-dependent utility functions may find themselves indifferent between accepting and rejecting an indivisible risky prospect. Bell (1988) showed that under these circumstances it is EU-enhancing for the decision maker to engage in a pre-decision side bet, accepting the indivisible risky prospect conditional upon winning the side bet. The side bet places the decision maker on the convex hull between the initial-wealth utility function and the utility function with risky-prospect-augmented wealth. We show that decision makers restricted to actuarially unfair side bets engage in a sequence of individually EU-enhancing side bets. This occurs because optimal stake size is modest for actuarially unfair side bets, whereby wealth remains within the interval of interim convexity upon losing the side bet. As optimal stake size falls strongly with each successive side-bet round, wealth remains within the interval of interim convexity. The EU enhancement conferred by each successive round is also strongly diminishing. Hence the side-bet sequence is eventually truncated when no further EU enhancement is available.

Suggested Citation

  • Kim Kaleva Kaivanto & David Alan Peel, 2017. "Pre-Decision Side-Bet Sequences," Working Papers 163327371, Lancaster University Management School, Economics Department.
    • Handle: RePEc:lan:wpaper:163327371
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    References listed on IDEAS

    as
    1. Philippe Delquié, 2008. "The Value of Information and Intensity of Preference," Decision Analysis, INFORMS, vol. 5(3), pages 129-139, September.
    2. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151-151.
    3. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279-279.
    4. David E. Bell, 1988. "The Value of Pre-Decision Side Bets for Utility Maximizers," Management Science, INFORMS, vol. 34(6), pages 797-800, June.
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    More about this item

    Keywords

    Expected Utility; risk aversion; side bets; rationality; indivisibility; discreteness; actuarial fairness;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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