  In this work, we consider the following family of two prover one-round games.
In the CHSH_q game, two parties are given x,y in F_q uniformly at random, and
each must produce an output a,b in F_q without communicating with the other.
The players' objective is to maximize the probability that their outputs
satisfy a+b=xy in F_q. This game was introduced by Buhrman and Massar (PRA
2005) as a large alphabet generalization of the celebrated CHSH game---which is
one of the most well-studied two-prover games in quantum information theory,
and which has a large number of applications to quantum cryptography and
quantum complexity.
  Our main contributions in this paper are the first asymptotic and explicit
bounds on the entangled and classical values of CHSH_q, and the realization of
a rather surprising connection between CHSH_q and geometric incidence theory.
On the way to these results, we also resolve a problem of Pawlowski and Winter
about pairwise independent Information Causality, which, beside being
interesting on its own, gives as an application a short proof of our upper
bound for the entangled value of CHSH_q.
