Sure-wins under coherence: A geometrical perspective

In this contribution we will present a generalization of de Finetti’s betting game in which a gambler is allowed to buy and sell unknown events’ betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sufficient, as in the original de Finetti’s frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent books on which sure-win is impossible. Our main results provide geometric characterizations of the space of all books which are jointly coherent with a fixed one. As a consequence we will also show that joint coherence is decidable.