Dutch Books and Conditional Probability

Abstract

An oddsmaker who does not update odds in accordance with conditional probability can be subjected to a sure loss. Such a losing situation is called a Dutch book. This is often presented as an argument for setting odds in accordance with conditional probability. We point out that if the strategic aspects of oddsmaking are taken into account (choice of odds is a strategic choice in games against bettors), then it is possible that in the equilibrium of the game, posted odds need not be updated ‘correctly.' This calls into question the role of such arguments in the foundations of decision theory.

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