Related papers: Gaming the Quantum
We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…
Poker has become a popular pastime all over the world. At any given moment one can find tens, if not hundreds, of thousands of players playing poker via their computers on the major on-line gaming sites. Indeed, according to the Vancouver,…
Classical game theory is a powerful tool focusing on optimized resource distribution, allocation and sharing in classical wired and wireless networks. As quantum networks are emerging as a means of providing true connectivity between…
In a recent paper, Eisert et al. presented a quantum mechanical generalization of Prisoner's Dilemma. They asserted that the maximally entangled game exhibits a unique Nash equilibrium which yields a pay-off equivalent to cooperative…
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…
The last two decades have witnessed a rapid development of quantum information processing, a new paradigm which studies the power and limit of "quantum advantages" in various information processing tasks. Problems such as when quantum…
In this paper, we introduce a framework of new mathematical representation of Game Theory, including static classical game and static quantum game. The idea is to find a set of base vectors in every single-player strategy space and to…
Quantum computers that process information by harnessing the remarkable power of quantum mechanics are increasingly being put to practical use. In the future, their impact will be felt in numerous fields, including in online casino games.…
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. In this…
A quantum financial approach to finite games of strategy is addressed, with an extension of Nash's theorem to the quantum financial setting, allowing for an entanglement of games of strategy with two-period financial allocation problems…
In quantum game theory, one of the most intriguing and important questions is, "Is it possible to get quantum advantages without any modification of the classical game?" The answer to this question so far has largely been negative. So far,…
With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that…
Most of atoms and molecule found in nature are capable of evolving towards and staying at their ground states, the lowest energy states. This paper offers a global optimization approach to understand the ground state as the equilibrium…
As quantum processors advance, the emergence of large-scale decentralized systems involving interacting quantum-enabled agents is on the horizon. Recent research efforts have explored quantum versions of Nash and correlated equilibria as…
Computing Nash equilibria of zero-sum games in classical and quantum settings is extensively studied. For general-sum games, computing Nash equilibria is PPAD-hard and the computing of a more general concept called correlated equilibria has…
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…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the…
In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)].…
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…
Quantum strategies have been successfully applied to game theory for years. However, as a reverse problem of game theory, the theory of mechanism design is ignored by physicists. In this paper, the theory of mechanism design is generalized…