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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…

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…

Correlated equilibria are sometimes more efficient than the Nash equilibria of a game without signals. We investigate whether the availability of quantum signals in the context of a classical strategic game may allow the players to achieve…

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of financial market in terms of quantum game…

Quantum game theory is the study of strategic behavior by agents with access to quantum technology. Broadly speaking, this technology can be employed in either of two ways: As part of a randomization device or as part of a communications…

We develop a resource-theoretical approach that allows us to quantify values of two-player, one-round cooperative games with quantum inputs and outputs, as well as values of quantum probabilistic hypergraphs. We analyse the quantum game…

We introduce quantum XOR games, a model of two-player one-round games that extends the model of XOR games by allowing the referee's questions to the players to be quantum states. We give examples showing that quantum XOR games exhibit a…

Energy cost is increasingly crucial in the modern computing industry with the wide deployment of large-scale machine learning models and language models. For the firms that provide computing services, low energy consumption is important…

There is an increasing interest in the role of macroscopic environments to our understanding of the basics of quantum theory. The knowledge of the implications of the quantum theory to other theories, especially to the statistical mechanics…

Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…

What happens when an infinite number of players play a quantum game? In this tutorial, we will answer this question by looking at the emergence of cooperation, in the presence of noise, in a one-shot quantum Prisoner's dilemma (QuPD). We…

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…

We will discuss the generalization of entropic uncertainty principles in terms of a game. The game involves k-players, each measuring one of k possible observables. The question is, what is the maximum number of players that can play such…

We address the question of when quantum entanglement is a useful resource for information processing tasks by presenting a new class of nonlocal games that are simple, direct, generalizations of the Clauser Horne Shimony Holt game. For some…

We study the influence of Unruh effect on quantum non-zero sum games. In particular, we investigate the quantum Prisoners' Dilemma both for entangled and unentangled initial states and show that the acceleration of the noninertial frames…

We study a quantum mechanical toy model that mimics some features of a quenched phase transition. Both by virtue of a time-dependent Hamiltonian or by changing the temperature of the bath we are able to show that even after classicalization…

Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…

Quantilized mean-field game models involve quantiles of the population's distribution. We study a class of such games with a capacity for ranking games, where the performance of each agent is evaluated based on its terminal state relative…

A contemporary technological milestone is to build a quantum device performing a computational task beyond the capability of any classical computer, an achievement known as quantum adversarial advantage. In what ways can the entanglement…

Quantum advantage, broadly understood as the ability of quantum systems to significantly outperform their classical counterparts, underpins current interest to quantum technologies and is a topic of active investigation. In many situations,…