Related papers: Quantum approach to Bertrand duopoly

The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…

We propose a simple yet rich model to extend the notions of Nash equilibria and correlated equilibria of strategic games to the quantum setting, in which we then study the relations between classical and quantum equilibria. Unlike the…

We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…

An approach towards quantum games is proposed that uses the unusual probabilities involved in EPR-type experiments directly in two-player games.

In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of…

We study the extension of classical games to the quantum domain, generated by the addition of one unitary strategy to two classical strategies of each player. The conditions that need to be met by unitary operations to ensure that the…

We present a two-party protocol for quantum gambling, a new task closely related to coin tossing. The protocol allows two remote parties to play a gambling game, such that in a certain limit it becomes a fair game. No unconditionally secure…

A game in which one player makes unitary transformations of a simple system, and another seeks to confound the resulting state by a randomly chosen action is analyzed carefully. It is shown that the second player can reduce any system to a…

Quantum Game Theory provides us with new tools for practising games and some other risk related enterprices like, for example, gambling. The two party gambling protocol presented by Goldenberg {\it et al} is one of the simplest yet still…

Using the representation introduced in \cite{frame}, an artificial game in quantum strategy space is proposed and studied. Although it has well-known classical correspondence, which has classical mixture strategy Nash Equilibrium states,…

Quantum game theory is a new interdisciplinary field between game theory and physical research. In this paper, we extend the classical inspection game into a quantum game version by quantizing the strategy space and importing entanglement…

We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric…

A fair gambling is hard to be made between two spatially separated parties without introducing a trusted third party. Here we propose a novel gambling protocol, which enables fair gambling between two distant parties without the help of a…

The aim of the paper is to examine the notion of simple Kantian equilibrium in $2 \times 2$ symmetric games and their quantum counterparts. We focus on finding the Kantian equilibrium strategies in the general form of the games. As a…

The two-players $N$ strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme (Phys. Rev. Lett. 83 (1999), 3077) are considered. Group theoretical methods are applied to the problem of finding a general form of gate…

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…

This paper investigates Nash equilibria in pure strategies for quantum approach to the Prisoner's Dilemma. The quantization process involves extending the classical game by introducing two additional unitary strategies. We consider five…

A quantum algorithm for an oracle problem can be understood as a quantum strategy for a player in a two-player zero-sum game in which the other player is constrained to play classically. I formalize this correspondence and give examples of…

In this work we propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free, and not fixed on its regular values. The developed quantum scheme is then used to study the expected…

The two-players N strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme [1] are considered. It is shown that in the case of maximal entanglement no nontrivial pure Nash equilibrium exists. The proof relies on simple…