A lower bound on the value of entangled binary games

A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is called entangled if the players are allowed to share a priori entanglement. It is well-known that the maximum winning probability (value) of entangled XOR-games (binary games in which the predetermined property depends only on the XOR of the two output bits) can be computed by a semidefinite program. In this paper we extend this result in the following sense; if a binary game is uniform, meaning that in an optimal strategy the marginal distributions of the output of each player are uniform, then its entangled value can be efficiently computed by a semidefinite program. We also introduce a lower bound on the entangled value of a general two-player one-round game; this bound depends on the size of the output set of each player and can be computed by a semidefinite program. In particular, we show that if the game is binary, $\omega_q$ is its entangled value, and $\omega_{sdp}$ is the optimum value of the corresponding semidefinite program, then $0.68\,\omega_{sdp} < \omega_q \leq \omega_{sdp}$.

Evolution of signalling systems with multiple senders and receivers

Sender–receiver games are simple, tractable models of information transmission. They provide a basic setting for the study the evolution of meaning. It is possible to investigate not only the equilibrium structure of these games but also the dynamics of evolution and learning—with sometimes surprising results. Generalizations of the usual binary game to interactions with multiple senders, multiple receivers or both provide the elements of signalling networks. These can be seen as the loci of information processing, group decisions, and teamwork.