Related papers: General quantum two-players games, their gate oper…
We show by counterexample that policy-gradient algorithms have no guarantees of even local convergence to Nash equilibria in continuous action and state space multi-agent settings. To do so, we analyze gradient-play in N-player general-sum…
This paper establishes the tractability of finding the optimal Nash equilibrium, as well as the optimal social solution, to a discrete congestion game using a gate-model quantum computer. The game is of the type originally posited by…
We show that the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length is NP-hard to approximate to within constant…
In the present letter, we propose a more general entangling operator to the quantization of Cournot economic model, in which players can access to a continuous set of strategies. By analyzing the relation between the von Neumann entropy of…
We extend the concept of a classical two-person static game to the quantum domain, by giving an Hilbert structure to the space of classical strategies and studying the Battle of the Sexes game. We show that the introduction of entangled…
The fundamental laws of quantum world upsets the logical foundation of classic physics. They are completely counter-intuitive with many bizarre behaviors. However, this paper shows that they may make sense from the perspective of a general…
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…
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…
We introduce Q-Nash, a quantum annealing algorithm for the NP-complete problem of Fnding pure Nash equilibria in graphical games. The algorithm consists of two phases. The first phase determines all combinations of best response strategies…
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…
The aim of this paper is to bring together the notions of quantum game and game isomorphism. The work is intended as an attempt to introduce a new criterion for quantum game schemes. The generally accepted requirement forces a quantum…
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…
In this paper, we generalize to three players the well-known CHSH quantum game. To do so, we consider all possible 3 variables Boolean functions and search among them which ones correspond to a game scenario with a quantum advantage (for a…
This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that…
Quantum games have attracted much attention in recent years due to their ability to solve decision-making dilemmas. The aim of this study is to extend previous work on quantum games by introducing a Mathematica package QEGS (Quantum…
Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic, no microscopic quantum agent is supposed. The reason for…
We propose a scheme for a quantum game based on performing an EPR type experiment and in which each player's spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the…
We investigate Nash Equilibrium in the quantum Battle of Sexes Game. We find the game has infinite Nash Equilibria and all of them leads to the asymmetry result. We also show that there is no unique but infinite Nash Equilibrium in it if we…
Landsburg method of classifying mixed Nash equilibria for maximally entangled Eisert-Lewenstein-Wilkens (ELW) game is analyzed with special emphasis on symmetries inherent to the problem. Nash equilibria for the original ELW game are…
We consider a system of single- or double integrator agents playing a generalized Nash game over a network, in a partial-information scenario. We address the generalized Nash equilibrium seeking problem by designing a fully-distributed…