Alladi Ramakrishnan Hall

Bayesian Games, Social Welfare Solutions, and Entanglement

Amit Mukherjee

Indian Statistical Institute, Kolkata

Interesting connection has been established between two apparently
unrelated concepts, namely, quantum nonlocality and Bayesian game
theory. It has been shown that nonlocal correlations in the form of
advice can outperform classical equilibrium strategies in common
interest Bayesian games and also in conflicting interest games.
However, classical equilibrium strategies can be of two types, fair and
unfair. Whereas in fair equilibrium, payoffs of different players are
same, in unfair case they differ. Advantage of nonlocal correlation has
been demonstrated over fair strategies. In this work we show that
quantum strategies can outperform even the unfair classical
equilibrium strategies. Furthermore, we call a quantum strategy as a
quantum social welfare solution if it is advantageous over a classical
equilibrium strategy in the sense that none of the players has to
sacrifice their classical equilibrium payoff, rather some have incentive
and at the same time it maximizes the sum of the payoffs over all
possible quantum advantageous strategies. Quantum state yielding
such a quantum social welfare solution is coined as quantum social
welfare advice. Interestingly, we show that any two-qubit pure entangled
states, even it is arbitrarily close to product state, can serve as quantum
social welfare advice in some Bayesian games. Our result, thus, gives
cognizance to the fact that every two-qubit entanglement is the best
resource for some operational tasks.

Related references:-
Phys. Rev. A 94, 032120 (2016);
arXiv:1703.02773.