461 research outputs found
Lifting the Veil of Ignorance: Personalizing the Marriage Contract
Symposium: Law and the New American Family Held at Indiana University School of Law - Bloomington Apr. 4, 199
Quantum correlations and Nash equilibria of a bi-matrix game
Playing a symmetric bi-matrix game is usually physically implemented by
sharing pairs of 'objects' between two players. A new setting is proposed that
explicitly shows effects of quantum correlations between the pairs on the
structure of payoff relations and the 'solutions' of the game. The setting
allows a re-expression of the game such that the players play the classical
game when their moves are performed on pairs of objects having correlations
that satisfy the Bell's inequalities. If players receive pairs having quantum
correlations the resulting game cannot be considered another classical
symmetric bi-matrix game. Also the Nash equilibria of the game are found to be
decided by the nature of the correlations.Comment: minor correction
Quantum correlation games
A new approach to play games quantum mechanically is proposed. We consider two players who perform measurements in an EPR-type setting. The payoff relations are defined as functions of correlations, i.e. without reference to classical or quantum mechanics. Classical bi-matrix games are reproduced if the input states are classical and perfectly anti-correlated, that is, for a classical correlation game. However, for a quantum correlation game, with an entangled singlet state as input, qualitatively different solutions are obtained. For example, the Prisoners' Dilemma acquires a Nash equilibrium if both players apply a mixed strategy. It appears to be conceptually impossible to reproduce the properties of quantum correlation games within the framework of classical games
Effects of Diversity on Multi-agent Systems: Minority Games
We consider a version of large population games whose agents compete for
resources using strategies with adaptable preferences. The games can be used to
model economic markets, ecosystems or distributed control. Diversity of initial
preferences of strategies is introduced by randomly assigning biases to the
strategies of different agents. We find that diversity among the agents reduces
their maladaptive behavior. We find interesting scaling relations with
diversity for the variance and other parameters such as the convergence time,
the fraction of fickle agents, and the variance of wealth, illustrating their
dynamical origin. When diversity increases, the scaling dynamics is modified by
kinetic sampling and waiting effects. Analyses yield excellent agreement with
simulations.Comment: 41 pages, 16 figures; minor improvements in content, added
references; to be published in Physical Review
Constructing quantum games from non-factorizable joint probabilities
A probabilistic framework is developed that gives a unifying perspective on
both the classical and the quantum games. We suggest exploiting peculiar
probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to
construct quantum games. In our framework a game attains classical
interpretation when joint probabilities are factorizable and a quantum game
corresponds when these probabilities cannot be factorized. We analyze how
non-factorizability changes Nash equilibria in two-player games while
considering the games of Prisoner's Dilemma, Stag Hunt, and Chicken. In this
framework we find that for the game of Prisoner's Dilemma even non-factorizable
EPR joint probabilities cannot be helpful to escape from the classical outcome
of the game. For a particular version of the Chicken game, however, we find
that the two non-factorizable sets of joint probabilities, that maximally
violates the Clauser-Holt-Shimony-Horne (CHSH) sum of correlations, indeed
result in new Nash equilibria.Comment: Revised in light of referee's comments, submitted to Physical Review
Multi-Player Quantum Games
Recently the concept of quantum information has been introduced into game
theory. Here we present the first study of quantum games with more than two
players. We discover that such games can possess a new form of equilibrium
strategy, one which has no analogue either in traditional games or even in
two-player quantum games. In these `pure' coherent equilibria, entanglement
shared among multiple players enables new kinds of cooperative behavior: indeed
it can act as a contract, in the sense that it prevents players from
successfully betraying one-another.Comment: 5 pages, 2 figs. Substantial revisons inc. new result
An Analysis of the Quantum Penny Flip Game using Geometric Algebra
We analyze the quantum penny flip game using geometric algebra and so
determine all possible unitary transformations which enable the player Q to
implement a winning strategy. Geometric algebra provides a clear visual picture
of the quantum game and its strategies, as well as providing a simple and
direct derivation of the winning transformation, which we demonstrate can be
parametrized by two angles. For comparison we derive the same general winning
strategy by conventional means using density matrices.Comment: 8 Pages, 1 Figure, accepted for publication in the Journal of
Physical Society of Japa
Quantum Matching Pennies Game
A quantum version of the Matching Pennies (MP) game is proposed that is
played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct
the quantum game without using the state vectors, while considering only the
quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We
embed the classical game within the quantum game such that the classical MP
game results when the quantum mechanical joint probabilities become
factorizable. We report new Nash equilibria in the quantum MP game that emerge
when the quantum mechanical joint probabilities maximally violate the
Clauser-Horne-Shimony-Holt form of Bell's inequality.Comment: Revised in light of referees' comments, submitted to Journal of the
Physical Society of Japan, 14 pages, 1 figur
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