Related papers: Strong isomorphism in Eisert-Wilkens-Lewenstein ty…
The explicit construction is presented of two-player game satisfying: (i) symmetry with respect to the permutation of the players; (ii) the existence of upper bound on total payoff following from Bell inequality; (iii) the existence of…
Effect of replacing the classical game object with a quantum object is analyzed. We find this replacement requires a throughout reformation of the framework of Game Theory. If we use density matrix to represent strategy state of players,…
We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…
We introduce a quantum version of the Game of Life and we use it to study the emergence of complexity in a quantum world. We show that the quantum evolution displays signatures of complex behaviour similar to the classical one, however a…
Iterated bipartite quantum games are implemented in terms of the discrete-time quantum walk on the line. Our proposal allows for conditional strategies, as two rational agents make a choice from a restricted set of two-qubit unitary…
We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…
A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary…
A quantum algorithm for an oracle problem can be understood as a quantum strategy for a player in a two-player zero-sum game in which the other player is constrained to play classically. I formalize this correspondence and give examples of…
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…
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,…
The concept of forming harmonious coalitions is introduced to both classical and quantum symmetric cooperative game. In both cases, players are motivated to form coalitions. Also, the main feature of the cooperative game is conserved.
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,…
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 and basic ideas of quantum game theory. Description of Giffen paradoxes…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
We investigate the quantization of games in which the players can access to a continuous set of classical strategies, making use of continuous-variable quantum systems. For the particular case of the Cournot's Duopoly, we find that, even…
Quantum mechanics courses focus mostly on its computational aspects. This alone does not provide the same depth of understanding as most physicists have of classical mechanics. The understanding of classical mechanics is significantly…
This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same…
We point out a flaw in the unfair case of the quantum Prisoner's Dilemma as introduced in the pioneering Letter "Quantum Games and Quantum Strategies" of Eisert, Wilkens and Lewenstein. It is not true that the so-called miracle move therein…
Game theory is a well established branch of mathematics whose formalism has a vast range of applications from the social sciences, biology, to economics. Motivated by quantum information science, there has been a leap in the formulation of…
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…