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A significant hurdle in the noisy intermediate-scale quantum (NISQ) era is identifying functional quantum circuits. These circuits must also adhere to the constraints imposed by current quantum hardware limitations. Variational quantum…
We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy…
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…
We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations…
In quantum game theory, one of the most intriguing and important questions is, "Is it possible to get quantum advantages without any modification of the classical game?" The answer to this question so far has largely been negative. So far,…
The aim of the paper is to examine the notion of simple Kantian equilibrium in $2 \times 2$ symmetric games and their quantum counterparts. We focus on finding the Kantian equilibrium strategies in the general form of the games. As a…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical variational algorithm that produces an upper-bound estimate of the ground-state energy of a Hamiltonian. As quantum computers become more powerful and go beyond the…
We define and study a collection of matroid isomorphism games corresponding to various axiomatic characterizations of matroids. These are nonlocal games played between two cooperative players. Each game is played on two matroids, and the…
We formulate a two-team linear quadratic stochas- tic dynamic game featuring two opposing teams each with decentralized information structures. We introduce the concept of mutual quadratic invariance (MQI), which, analogously to quadratic…
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 study a generalization of the Mermin-Peres magic square game to arbitrary rectangular dimensions. After exhibiting some general properties, these rectangular games are fully characterized in terms of their optimal win probabilities for…
The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum…
We introduce a notion of strategies based on averaging for nonlocal games in quantum information theory. These so-called statistical strategies come in a commuting type and a more specific spatial type, which are respectively special cases…
Game theory is playing more and more important roles in understanding complex systems and in investigating intelligent machines with various uncertainties. As a starting point, we consider the classical two-player zero-sum linear-quadratic…
We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric…
The behavior of entangled quantum systems can generally not be explained as being determined by shared classical randomness. In the first part of this paper, we propose a simple game for n players demonstrating this non-local property of…
Noisy intermediate-scale quantum computers (NISQ computers) are now readily available, motivating many researchers to experiment with Variational Quantum Algorithms (VQAs). Among them, the Quantum Approximate Optimization Algorithm (QAOA)…
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…
Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…