Playing games with quantum entanglement and other correlations
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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 in the sense of Nash 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 demonstrate that even separable quantum states can create new, genuinely quantum equilibria in games, which 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. These insights also illuminate and significantly differentiate the existing hierarchy of "legitimate notions of equilibrium" in Bayesian games.
[Based on arXiv:1605.07896, and arXiv:2607.09477 with Yaqing Wang and Giannicola Scarpa]