Abstract
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 sucient, 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 xed one. As
a consequence we will also show that joint coherence is decidable.