Classical and Quantum Equilibria in Bayesian Games ⋆

Yaqing Xy Wang, Giannicola Scarpa, Andreas Winter

Bayesian games, also known as games of incomplete information, are a fruitful arena for exploring the impact of correlations on a set of independent agents (players) via the game equilibria to which they give rise. It was realised some time ago that quantum states shared between the players can lead to new and beneficial equilibria, compared to classical correlation. While until now examples of this effect required an entangled state, here we show that even separable states can create new, genuinely quantum equilibria in games, that are advantageous with respect to all classically correlated equilibria. This shows that non-classical correlations beyond entanglement are indeed a resource, even in otherwise entirely classical situations. Our result brings quantum advantage in games significantly closer to possible realisation.

Neal Solmeyer, Ricky Dixon, Radhakrishnan Balu

Igal Milchtaich

Mátyás Koniorczyk, András Bodor, Miklós Pintér

We analyze the difference between ex ante and ex post equilibria in classical games played with the assistance of a nonlocal (quantum or no-signaling) resource. In physics, the playing of these games is known as performing bipartite Bell-type experiments. By analyzing the Clauser-Horn-Shimony-Holt game, we find a constructive procedure to find two-person Bayesian games with a nonlocal (i.e., no-signaling, and, in many cases, quantum) advantage. Most games of this kind known from the literature can be constructed along this principle, and share the property that their relevant ex ante equilibria are ex post equilibria as well. We introduce here a different type of game, based on the Bell theorem by V\'ertesi and Bene, which does not have the latter property: The ex ante and ex post equilibria differ.

Haozhen Situ

Piotr Frąckiewicz