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Despite the successes of recent works in quantum reinforcement learning, there are still severe limitations on its applications due to the challenge of encoding large observation spaces into quantum systems. To address this challenge, we…
XOR games are the simplest model in which the nonlocal properties of entanglement manifest themselves. When there are two players, it is well known that the bias --- the maximum advantage over random play --- of entangled players can be at…
Game theory has by now found numerous applications in various fields, including economics, industry, jurisprudence, and artificial intelligence, where each player only cares about its own interest in a noncooperative or cooperative manner,…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
This paper explores the use of Generative Pre-trained Transformers (GPT) in strategic game experiments, specifically the ultimatum game and the prisoner's dilemma. I designed prompts and architectures to enable GPT to understand the game…
Quantum generalizations of conventional games broaden the range of available strategies, which can help improve outcomes for the participants. With many players, such quantum games can involve entanglement among many states which is…
By designing a proper unitary operator U, we synthesize NMR analogues of Einstein-Podolsky-Rosen states (pseudo-EPR states) using generalized Grover's algorithm on a nuclear magnetic resonance (NMR) quantum computer. Experiments also…
We investigate the consequences of allowing players to adopt strategies which take advantage of quantum randomization devices. In games of full information, the resulting equilibria are always correlated equilibria, but not all correlated…
We give a concise and self-contained introduction to the theory of Quantum Games by reviewing the seminal works of Meyer, Eisert-Wilkens-Lewenstein, Marinatto-Weber and Landsburg, which initiated the study of this field. By generalizing…
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…
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…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
The study focuses on strategic-form games extended in the Eisert-Wilkens-Lewenstein scheme by two unitary operations. Conditions are determined under which the pair of unitary operators, along with classical strategies, form a game…
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…
Non-local games are studied in quantum information because they provide a simple way for proving the difference between the classical world and the quantum world. A non-local game is a cooperative game played by 2 or more players against a…
Recent results showed it was possible to determine if a modest size 3XOR game has a perfect quantum strategy. We build on these and give an explicit polynomial time algorithm which constructs such a perfect strategy or refutes its…
The last two decades have witnessed a rapid development of quantum information processing, a new paradigm which studies the power and limit of "quantum advantages" in various information processing tasks. Problems such as when quantum…
In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a…
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…
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…