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The paper is devoted to quantization of extensive games with the use of both the Marinatto-Weber and the Eisert-Wilkens-Lewenstein concept of quantum game. We revise the current conception of quantum ultimatum game and we show why the…
We give a strict mathematical description for a refinement of the Marinatto-Weber quantum game scheme. The model allows the players to choose projector operators that determine the state on which they perform their local operators. The game…
We generalize a concept of classical finite extensive game to make it useful for application of quantum objects. The generalization extends a quantum realization scheme of static games to any finite extensive game. It represents an…
Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…
Theory of quantum games is relatively new to the literature and its applications to various areas of research are being explored. It is a novel interpretation of strategies and decisions in quantum domain. In the earlier work on quantum…
Quantization becomes a new way to study classical game theory since quantum strategies and quantum games have been proposed. In previous studies, many typical game models, such as prisoner's dilemma, battle of the sexes, Hawk-Dove game,…
We develop a rigorous mathematical framework for quantum game theory applied to static 2x2 games, extending classical concepts to the quantum setting where players may employ arbitrary unitary operations (pure strategies) or probability…
Attention to the very physical aspects of information characterizes the current research in quantum computation, quantum cryptography and quantum communication. In most of the cases quantum description of the system provides advantages over…
We present a quantum approach to a signaling game; a special kind of extensive games of incomplete information. Our model is based on quantum schemes for games in strategic form where players perform unitary operators on their own qubits of…
Recently Marinatto and Weber introduced an interesting new scheme for quantizing games, and applied their scheme to the famous game 'Battle of the Sexes'. In this Comment we make two observations: (a) the overall quantization scheme is…
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 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…
In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)].…
Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess a new form of equilibrium strategy, one…
We propose a concept of quantum extensive-form games, which is a quantum extension of classical extensive-form games. Extensive-form games is a general concept of games such as Go, Shogi, and chess, which have triggered the recent AI…
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…
Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. In this…
The Marinatto-Weber approach to quantum game is a straightforward way to apply the power of quantum mechanics to classical game theory. In the simplest case, the quantum scheme is that players manipulate their own qubits of a two-qubit…
Quantum guessing games form a versatile framework for studying different tasks of information processing. A quantum guessing game with posterior information uses quantum systems to encode messages and classical communication to give partial…
Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the…