  Entanglement is of paramount importance in quantum information theory. Its
supremacy over classical correlations has been demonstrated in numerous
information theoretic protocols. Here we study possible adequacy of quantum
entanglement in Bayesian game theory, particularly in social welfare solution
(SWS), a strategy which the players follow to maximize the sum of their
payoffs. Given a multi-partite quantum state as an advice, players can come up
with several correlated strategies by performing local measurements on their
parts of the quantum state. A quantum strategy is called quantum-SWS if it is
advantageous over a classical equilibrium (CE) strategy in the sense that none
of the players has to sacrifice their CE-payoff rather some have incentive and
at the same time it maximizes the sum of all players' payoffs over all possible
quantum advantageous strategies. Quantum state yielding such a quantum-SWS is
called a quantum social welfare advice (SWA). We show that any two-qubit pure
entangled state, even if it is arbitrarily close to a product state, can serve
as quantum-SWA in some Bayesian game. Our result, thus, gives cognizance to the
fact that every two-qubit pure entanglement is the best resource for some
operational task.
