256 research outputs found
A non-cooperative Pareto-efficient solution to a one-shot Prisoner's Dilemma
The Prisoner's Dilemma is a simple model that captures the essential
contradiction between individual rationality and global rationality. Although
the one-shot Prisoner's Dilemma is usually viewed simple, in this paper we will
categorize it into five different types. For the type-4 Prisoner's Dilemma
game, we will propose a self-enforcing algorithmic model to help
non-cooperative agents obtain Pareto-efficient payoffs. The algorithmic model
is based on an algorithm using complex numbers and can work in macro
applications.Comment: 14 pages, 3 figure
Quantum Bayesian implementation and revelation principle
Bayesian implementation concerns decision making problems when agents have incomplete information. This paper proposes that the traditional sufficient conditions for Bayesian implementation shall be amended by virtue of a quantum Bayesian mechanism. In addition, by using an algorithmic Bayesian mechanism, this amendment holds in the macro world. More importantly, we find that the revelation principle is not always right by using the quantum and algorithmic Bayesian mechanisms.
Two-agent Nash implementation: A new result
[J. Moore and R. Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099]
and [B. Dutta and A. Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128]
are two important papers on two-agent Nash implementation. Recently, [H. Wu,
Quantum mechanism helps agents combat "bad" social choice rules.
\emph{International Journal of Quantum Information}, 2010 (accepted).
abs/1002.4294 ] broke through traditional results on Nash implementation with
three or more agents. In this paper, we will investigate two-agent Nash
implementation by virtue of Wu's quantum mechanism. The main result is: A
two-agent social choice rule that satisfies Condition will no longer be
Nash implementable if an additional Condition is satisfied.
Moreover, according to a classical two-agent algorithm, this result holds not
only in the quantum world, but also in the macro world.Comment: 15 pages, 4 figure
Subgame perfect implementation: A new result
This paper concerns what will happen if quantum mechanics is concerned in
subgame perfect implementation. The main result is: When additional conditions
are satisfied, the traditional characterization on subgame perfect
implementation shall be amended by virtue of a quantum stage mechanism.
Furthermore, by using an algorithmic stage mechanism, this amendment holds in
the macro world too.Comment: 16 pages, 3 figure
On the justification of applying quantum strategies to the Prisoners' Dilemma and mechanism design
The Prisoners' Dilemma is perhaps the most famous model in the field of game
theory. Consequently, it is natural to investigate its quantum version when one
considers to apply quantum strategies to game theory. There are two main
results in this paper: 1) The well-known Prisoners' Dilemma can be categorized
into three types and only the third type is adaptable for quantum strategies.
2) As a reverse problem of game theory, mechanism design provides a better
circumstance for quantum strategies than game theory does.Comment: 6 pages, 2 figure
Quantum mechanism helps agents combat Pareto-inefficient social choice rules
Quantum strategies have been successfully applied in game theory for years. However, as a reverse problem of game theory, the theory of mechanism design is ignored by physicists. In this paper, we generalize the classical theory of mechanism design to a quantum domain and obtain two results: 1) We find that the mechanism in the proof of Maskin's sufficiency theorem is built on the Prisoners' Dilemma. 2) By virtue of a quantum mechanism, agents who satisfy a certain condition can combat Pareto-inefficient social choice rules instead of being restricted by the traditional mechanism design theory.Quantum games; Mechanism design; Implementation theory; Nash implementation; Maskin monotonicity
Two-agent Nash implementation: A new result
[Moore and Repullo, \emph{Econometrica} \textbf{58} (1990) 1083-1099] and [Dutta and Sen, \emph{Rev. Econom. Stud.} \textbf{58} (1991) 121-128] are two fundamental papers on two-agent Nash implementation. Both of them are based on Maskin's classic paper [Maskin, \emph{Rev. Econom. Stud.} \textbf{66} (1999) 23-38]. A recent work [Wu, http://arxiv.org/abs/1002.4294, \emph{Inter. J. Quantum Information}, 2010 (accepted)] shows that when an additional condition is satisfied, the Maskin's theorem will no longer hold by using a quantum mechanism. Furthermore, this result holds in the macro world by using an algorithmic mechanism. In this paper, we will investigate two-agent Nash implementation by virtue of the algorithmic mechanism. The main result is: The sufficient and necessary conditions for Nash implementation with two agents shall be amended, not only in the quantum world, but also in the macro world.Quantum game theory; Mechanism design; Nash implementation.
A classical algorithm to break through Maskin's theorem for small-scale cases
Quantum mechanics has been applied to game theory for years. A recent work [H. Wu, Quantum mechanism helps agents combat ``bad'' social choice rules. \emph{International Journal of Quantum Information}, 2010 (accepted). Also see http://arxiv.org/pdf/1002.4294v3] has generalized quantum mechanics to the theory of mechanism design (a reverse problem of game theory). Although the quantum mechanism is theoretically feasible, agents cannot benefit from it immediately due to the restriction of current experimental technologies. In this paper, a classical algorithm is proposed to help agents combat ``bad'' social choice rules immediately. The algorithm works well when the number of agents is not very large (e.g., less than 20). Since this condition is acceptable for small-scale cases, it can be concluded that the Maskin's sufficiency theorem has been broken through for small-scale cases just right now. In the future, when the experimental technologies for quantum information are commercially available, the Wu's quantum mechanism will break through the Maskin's sufficiency theorem completely.Quantum games; Prisoners' Dilemma; Mechanism design.
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