633 research outputs found
Social optimality in quantum Bayesian games
A significant aspect of the study of quantum strategies is the exploration of
the game-theoretic solution concept of the Nash equilibrium in relation to the
quantization of a game. Pareto optimality is a refinement on the set of Nash
equilibria. A refinement on the set of Pareto optimal outcomes is known as
social optimality in which the sum of players' payoffs are maximized. This
paper analyzes social optimality in a Bayesian game that uses the setting of
generalized Einstein-Podolsky-Rosen experiments for its physical
implementation. We show that for the quantum Bayesian game a direct connection
appears between the violation of Bell's inequality and the social optimal
outcome of the game and that it attains a superior socially optimal outcome.Comment: 12 pages, revise
The equivalence of Bell's inequality and the Nash inequality in a quantum game-theoretic setting
The interaction of competing agents is described by classical game theory. It
is now well known that this can be extended to the quantum domain, where agents
obey the rules of quantum mechanics. This is of emerging interest for exploring
quantum foundations, quantum protocols, quantum auctions, quantum cryptography,
and the dynamics of quantum cryptocurrency, for example. In this paper, we
investigate two-player games in which a strategy pair can exist as a Nash
equilibrium when the games obey the rules of quantum mechanics. Using a
generalized Einstein-Podolsky-Rosen (EPR) setting for two-player quantum games,
and considering a particular strategy pair, we identify sets of games for which
the pair can exist as a Nash equilibrium only when Bell's inequality is
violated. We thus determine specific games for which the Nash inequality
becomes equivalent to Bell's inequality for the considered strategy pair.Comment: 18 pages, revise
Analyzing three-player quantum games in an EPR type setup
We use the formalism of Clifford Geometric Algebra (GA) to develop an
analysis of quantum versions of three-player non-cooperative games. The quantum
games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting.
In this setting, the players' strategy sets remain identical to the ones in the
mixed-strategy version of the classical game that is obtained as a proper
subset of the corresponding quantum game. Using GA we investigate the outcome
of a realization of the game by players sharing GHZ state, W state, and a
mixture of GHZ and W states. As a specific example, we study the game of
three-player Prisoners' Dilemma.Comment: 21 pages, 3 figure
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