Game theory is used today in a wide range of areas such as economics, social sciences, biology and philosophy, gives a mathematical framework for describing a situation of conflict or cooperation between intelligent rational players.  

The central goal is to predict the outcome of the process. In the early 1950s, John Nash showed that the strategies adopted by the players form an equilibrium point (so-called Nash equilibrium) for which none of the players has any incentive to change strategy.

Quantum mechanics describes the physics of small objects such as particles and atoms and predicts a vast range of astonishing and often strikingly counter-intuitive phenomena, such as quantum nonlocality. In the 1960s, John Stewart Bell demonstrated that the predictions of quantum mechanics are incompatible with the principle of locality, that is, the fact that an object can be influenced directly only by its immediate surroundings and not by distant events. In particular, when remote observers perform measurements on a pair of entangled quantum particles, such as photons, the results of these measurements are highly correlated. In fact, these correlations are so strong that they cannot be explained by any physical theory respecting the principle of locality. Hence quantum mechanics is a nonlocal theory, and the fact that Nature is nonlocal has been confirmed in numerous experiments.

What links them is the same concepts appearing in both fields. For instance, the physical notion of locality appears naturally in games where players adopt a classical strategy. In fact the principle of locality sets a fundamental limit to the performance achievable by classical players (that is, bound by the rules of classical physics). 

Bringing quantum mechanics into the game, the researchers showed that players who can use quantum resources, such as entangled quantum particles, can outperform classical players. That is, quantum players achieve better performance than any classical player ever could.

Let's consult our old friends Alice and Bob:

Bell inequality test scenario. A source distributes physical resources to two distant players, Alice and Bob. Each player receives a question, denoted X1 for Alice and X2 for Bob, and should then provide an answer, denoted A1 for Alice and A2 for Bob. Credit: 

Dr. Nicolas Brunner and mathematics Professor Noah Linden of the University of Bristol worked together to uncover the deep and unexpected connection between game theory and quantum physics - the link between Bell nonlocality and Bayesian games.

Brunner said: "Once in a while, connections are established between topics which seem, on the face of it, to have nothing in common. Such new links have potential to trigger significant progress and open entirely new avenues for research.  

"Such an advantage could, for instance, be useful in auctions which are well described by the type of games that we considered. Therefore, our work not only opens a bridge between two remote scientific communities, but also opens novel possible applications for quantum technologies."

Citation: Nicolas Brunner  &  Noah Linden, 'Connection between Bell nonlocality and Bayesian game theory', Nature Communications 4, Article number: 2057 doi:10.1038/ncomms3057