Related papers: A new quantum scheme for normal-form games

Recently, a standardized framework was proposed for introducing quantum-inspired moves in mathematical games with perfect information and no chance. The beauty of quantum games-succinct in representation, rich in structures, explosive in…

We study how strategic interaction can arise from controlled quantum dynamics rather than being imposed as an external mathematical structure. We introduce a class of interaction-defined quantum games in which players are represented by…

An example of the macroscopic game of two partners consisting of two classical games played simultaneously with special dependence of strategies is considered. The average profit of each partner is equal to the average profit obtained in…

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.

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…

We show that it is perfectly possible to play 'restricted' two-players, two-strategies quantum games proposed originally by Marinatto and Weber having as the only equipment a pack of 10 cards. The 'quantum board' of such a model of these…

Theory of quantum games is a new area of investigation that has gone through rapid development during the last few years. Initial motivation for playing games, in the quantum world, comes from the possibility of re-formulating quantum…

We introduce a quantum version of the Game of Life and we use it to study the emergence of complexity in a quantum world. We show that the quantum evolution displays signatures of complex behaviour similar to the classical one, however a…

Quantum games embody non-intuitive consequences of quantum phenomena, such as entanglement and contextuality. The Mermin-Peres game is a simple example, demonstrating how two players can utilise shared quantum information to win a no -…

This paper presents a new mathematical formalism that describes the quantization of games. The study of so-called quantum games is quite new, arising from a seminal paper of D. Meyer \cite{Meyer} published in Physics Review Letters in 1999.…

We initiate a study of random instances of nonlocal games. We show that quantum strategies are better than classical for almost any 2-player XOR game. More precisely, for large n, the entangled value of a random 2-player XOR game with n…

Games are useful tools for introducing new concepts to students. This paper describes a competitive two-player game for sophomore students in a modern physics survey course or junior/senior students in an introductory quantum mechanics…

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that…

We reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. Two of the authors have recently proposed a quantum description of financial market in terms…

In the standard approach to quantum games, players' moves are local unitary transformations on an entangled state that is subsequently measured. Players' payoffs are then obtained as expected values of the entries in the payoff matrix of…

We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable…

We develop a generic computational model that can be used effectively for establishing the existence of winning strategies for concrete finite combinatorial games. Our modelling is (equational) logic-based involving advanced techniques from…

We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction…

In this paper, we propose a Quantum variation of combinatorial games, generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff. A combinatorial game is a two-player game with no chance and no hidden information, such as Go or Chess. In…

We introduce a new solution concept for bounded rational agents in finite normal-form general-sum games called Generalized Quantal Response Equilibrium (GQRE) which generalizes Quantal Response Equilibrium~\citep{mckelvey1995quantal}. In…