Sensitivity analysis of a sequential decision problem with learning

  • Alfred Müller
  • Marco Scarsini


We consider the optimization problem of a decision maker facing a sequence of coin tosses with an initially unknown probability Θ for heads. Before each toss she bets on either heads or tails and she wins one euro if she guesses correctly, otherwise she loses one euro. We investigate the effect of changes in the distribution of Θ on the expected optimal gain of the decision maker. Using techniques from Bayesian dynamic programming we will show that under the assumption of a beta distribution for the prior a riskier prior implies higher expected gains. The rationale for this is that a riskier prior allows better learning and provides higher informational value to the observations. We will also consider the case of a risk-sensitive decision maker in a two-period model.

Key words: Coin tossing Bayesian dynamic programming beta distribution conjugate prior risk aversion stochastic comparison 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Alfred Müller
    • 1
  • Marco Scarsini
    • 2
  1. 1.Institut für Wirtschaftstheorie und Operations Research, Universität Karlsruhe, Geb. 20.21, D-76128 Karlsruhe, Germany (e-mail:
  2. 2.Dipartimento di Statistica e Matematica Applicata, Università di Torino, Piazza Arbarello 8, 10122 Torino, Italy (email:

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