Abstract
Entanglement is of paramount importance in quantum information theory. Its supremacy over classical correlations has been demonstrated in a 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 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 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.
Highlights
Game theory is the study of human conflict and cooperation within a competitive situation
Each decision maker is considered as a player with a set of possible actions and each one has preference over certain actions
In this work we show that any two-qubit pure entangled state, less entanglement it may have, can produce quantum-social welfare solution (SWS) for some Bayesian game
Summary
Game theory is the study of human conflict and cooperation within a competitive situation It has been widely used in various social and behavioral sciences, e.g., economics [1], political sciences [2], biological phenomena [3], as well as logic, computer science, and psychology [4]. Psychological evidence shows that rather than pursuing solely their own payoffs, players may consider additional social goals Such social behavior of the players may result different types of ‘fairness equilibrium’ solution. The players can come up with correlations generated from the quantum advice by performing local measurements on their respective parts of quantum system and can follow a correlated strategy. Our main results are presented in Sec. [4], and in Sec. [5] we present a brief discussion
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