Colloquium, Mathematical Sciences

Abstract: Bayesian games, also known as games with incomplete information, are a fruitful arena for testing out 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 (of which we will review one) required an entangled state, we can now 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, and it shows that the weakest form of non-classical correlation (aka quantum discord) can be a resource in multi-agent scenarios. It also illuminates and significantly differentiates the existing hierarchy of "legitimate notions of equilibrium" in Bayesian games. [Based on arXiv:1605.07896 and forthcoming work with Y. Wang and G. Scarpa]