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We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There…

Effects of quantum and classical correlations on game theory are studied to clarify the new aspects brought into game theory by the quantum mechanical toolbox. In this study, we compare quantum correlation represented by a maximally…

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…

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…

We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these…

We consider a coalitional game with the same payoff for all players. To maximize the payoff, the players need to use one collective strategy, if all players are in certain states, and the other strategy otherwise. The current state of each…

A quantum algorithm succeeds not because the superposition principle allows 'the computation of all values of a function at once' via 'quantum parallelism,' but rather because the structure of a quantum state space allows new sorts of…

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…

A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy,…

Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player-two…

Game theory is central to the understanding of competitive interactions arising in many fields, from the social and physical sciences to economics. Recently, as the definition of information is generalized to include entangled quantum…

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…

Conventionally the total correlations within a quantum system are quantified through distance-based expressions such as the relative entropy or the square-norm. Those expressions imply that a quantum state can contain both classical and…

We investigate the consequences of allowing players to adopt strategies which take advantage of quantum randomization devices. In games of full information, the resulting equilibria are always correlated equilibria, but not all correlated…

In this paper we show that, given $k\geq 3$, there exist $k$-player quantum XOR games for which the entangled bias can be arbitrarily larger than the bias of the game when the players are restricted to separable strategies. In particular,…

It is known that repeated gambling over the outcomes of independent and identically distributed (i.i.d.) random variables gives rise to alternate operational meaning of entropies in the classical case in terms of the doubling rates. We give…

We introduce a quantum cloning game in which $k$ separate collaborative parties receive a classical input, determining which of them has to share a maximally entangled state with an additional party (referee). We provide the optimal winning…

We study the scenario where the players of a classical complete information game initially share an entangled pure quantum state. Each player may perform arbitrary local operations on his own qubits, but no direct communication is allowed.…

The noncooperative Nash equilibrium solution of classical games corresponds to a rational expectations attitude on the part of the players. However, in many cases, games played by human players have outcomes very different from Nash…

Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…