Related papers: Analysis of two-player quantum games in an EPR set…
We present a scheme for playing quantum repeated 2x2 games based on the Marinatto and Weber's approach to quantum games. As a potential application, we study twice repeated Prisoner's Dilemma game. We show that results not available in…
The non-local game scenario provides a powerful framework to study the limitations of classical and quantum correlations, by studying the upper bounds of the winning probabilities those correlations offer in cooperation games where…
We present a consistent formulation of quantum game theory that accommodates all possible strategies in Hilbert space. The physical content of the quantum strategy is revealed as a family of classical games representing altruistic game play…
The Eisert et al. maximally entangled quantum game is studied within the framework of (elementary) group theory. It is shown that the game can be described in terms of real Hilbert space of states. It is also shown that the crucial…
Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…
We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
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 characterize exact, and approximate, optimality of games that players can interact with using quantum strategies. In comparison to a previous work of the author, arXiv: 2311.12887, which applied a 2016 framework due to Ostrev for…
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 -…
We consider quantum variants of Parrondo games on low-dimensional Hilbert spaces. The two games which form the Parrondo game are implemented as quantum walks on a small cycle of length $M$. The dimension of the Hilbert space is $2M$. We…
Quantum games with incomplete information can be studied within a Bayesian framework. We analyze games quantized within the EWL framework [Eisert, Wilkens, and Lewenstein, Phys Rev. Lett. 83, 3077 (1999)]. We solve for the Nash equilibria…
This paper introduces a geometric framework for analyzing power relations in games, independent of their strategic form. We define a canonical preference space where each player's relational stance is a normalized vector. This model…
We introduce a method of analyzing entanglement enhanced quantum games on regular lattices of agents. Our method is valid for setups with periodic and non-periodic boundary conditions. To demonstrate our approach we study two different…
In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium…
Coordination and cooperation are among the most important issues of game theory. Recently, the attention turned to game theory on graphs and social networks. Encouraged by interesting results obtained in quantum evolutionary game analysis,…
It is shown that experiments of the Einstein-Podolski-Rosen type are the natural consequence of the groupoid approach to noncommutative unification of general relativity and quantum mechanics. The geometry of this model is determined by the…
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…
The numbers game is a one-player game played on a finite simple graph with certain ``amplitudes'' assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…
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…