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A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are…

The discontinuous dependence of the properties of a quantum game on its entanglement has been shown up to be very much like phase transitions viewed in the entanglement-payoff diagram [J. Du et al., Phys. Rev. Lett, 88, 137902 (2002)]. In…

We examine the classical contents of quantum games. It is shown that a quantum strategy can be interpreted as a classical strategies with effective density-dependent game matrices composed of transposed matrix elements. In particular,…

We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this…

We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner's Dilemma, Battle of the Sexes and Chicken, through three prototype…

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…

We study two forms of a symmetric cooperative game played by three players, one classical and other quantum. In its classical form making a coalition gives advantage to players and they are motivated to do so. However in its quantum form…

A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given. Decoherence in other types of quantum games is…

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to…

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…

In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon…

Theory of quantum games is relatively new to the literature and its applications to various areas of research are being explored. It is a novel interpretation of strategies and decisions in quantum domain. In the earlier work on quantum…

A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…

We investigate quantum strategy in moving frames by considering Prisoner's Dilemma and propose four thresholds of $\gamma$ for two players to determine their \textit{Nash Equilibria}. Specially, an interesting phenomenon appears in…

Artificial intelligence and robotic competitions are accompanied by a class of game paradigms in which each player privately commits a strategy to a game system which simulates the game using the collected joint strategy and then returns…

The quantization of 2-players N-strategies games is considered. The general form of gate operator is determined under the assumption that the classical pure strategies are contained in the set of pure quantum ones.

We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…

Equilibrium solution concepts of normal-form games, such as Nash equilibria, correlated equilibria, and coarse correlated equilibria, describe the joint strategy profiles from which no player has incentive to unilaterally deviate. They are…

This paper unifies the concepts of evolutionary games and quantum strategies. First, we state the formulation and properties of classical evolutionary strategies, with focus on the destinations of evolution in 2-player 2-strategy games. We…

In this paper I quantize the stag hunt game in the framework proposed by Marinatto and Weber which, is introduced to quantize the Battle of the Sexes game and gives a general quntization scheme of various game theories. Then I discuss the…