Dutch Books: Avoiding Strategic and Dynamic Complications, and a Comonotic Extension

This paper formalizes de finetti’s book-making principle as a static individual preference condition. It thus avoids the confounding strategic and dynamic effects of modern formulations that consider games with sequential moves between a bookmaker and a bettor. This paper next shows that the book-making principle, commonly used to justify additive subjective probabilities, can be modified to agree with nonadditive probabilities. The principle is simply restricted to comonotonic subsets which, as usual, leads to an axiomatization of rank-dependent utility theory. Typical features of rank-dependence such as hedging, ambiguity aversion, and pessimism and optimism can be accommodated. The model leads to suggestions for a simplified empirical measurement of nonadditive probabilities.