719 research outputs found
Quantum Auctions: Facts and Myths
Quantum game theory, whatever opinions may be held due to its abstract physical formalism, have already found various applications even outside the orthodox physics domain. In this paper we introduce the concept of a quantum auction, its advantages and drawbacks. Then we describe the models that have already been put forward. A general model involves Wigner formalism and infinite dimensional Hilbert spaces - we envisage that the implementation might not be an easy task. But a restricted model advocated by the Hewlett-Packard group (Hogg et al) seems to be much easier to implement. We focus on problems related to combinatorial auctions and technical assumptions that are made. Powerful quantum algorithms for finding solutions would extend the range of possible applications. Quantum strategies, being qubits, can be teleported but are immune from cloning - therefore extreme privacy of agent's activity could in principle be guaranteed. Then we point out some key problem that have to be solved before commercial use would be possible. With present technology, optical networks, single photon sources and detectors seems to be sufficient for experimental realization in the near future.
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
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
Decision Making and Trade without Probabilities
This paper studies trade in a first-price sealed-bid auction where agents know only a range of possible payoffs. The setting is one in which a lemons problem arises, so that if agents have common risk preferences and common priors, then expected utility theory leads to a prediction of no trade. In contrast, we develop a model of rational non-probabilistic decision making, under which trade can occur because not bidding is a weakly dominated strategy. We use a laboratory experiment to test the predictions of both models, and also of models of expected utility with heterogeneous priors and risk preferences. We find strong support for the rational non-probabilistic model
Dagstuhl News January - December 2002
"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic
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