In the present study a notion of Dutch Book in a rank-dependent framework is presented. A comonotonic Dutch Book is a system of bets that reveals an incoherent behavior towards comonotonic gambles. The aim of the paper is to present de Finetti's Dutch Bookmaking theorem in a non-additive version. The result is that the theorem shows precisely to what degree non-additive probabilities are prone to bookmaking: they are to non-comonotonic, but not to comonotonic probabilities. Our result provides a new argument in favor of rank-dependent models.

Co-author Peter P. Wakker