Related papers: Quantum realization of extensive games
In the context of quantum information theory, "quantization" of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of…
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…
We investigate a multi-player and multi-choice quantum game. We start from two-player and two-choice game and the result is better than its classical version. Then we extend it to N-player and N-choice cases. In the quantum domain, we…
In this paper we define the canonical mixed extension of a decision form game. We motivate the necessity to introduce this concept and we show several examples about the new concept. In particular we focus our study upon the mixed…
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…
The noncooperative Nash equilibrium solution of classical games corresponds to a rational expectations attitude on the part of the players. However, in many cases, games played by human players have outcomes very different from Nash…
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that…
In the flavour of categorical quantum mechanics, we extend nonlocal games to allow quantum questions and answers, using quantum sets (special symmetric dagger Frobenius algebras) and the quantum functions of Musto, Reutter, and Verdon…
A classic model to study strategic decision making in multi-agent systems is the normal-form game. This model can be generalised to allow for an infinite number of pure strategies leading to continuous games. Multi-objective normal-form…
Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…
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. On grounds…
Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite…
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,…
Here we study multiplayer linear games, a natural generalization of XOR games to multiple outcomes. We generalize a recently proposed efficiently computable bound, in terms of the norm of a game matrix, on the quantum value of 2-player…
The purpose of this paper is to show how a class of classical linear stochastic systems can be physically implemented using quantum optical components. Quantum optical systems typically have much higher bandwidth than electronic devices,…
Our purpose is to focus attention on a new criterion for quantum schemes by bringing together the notions of quantum game and game isomorphism. A quantum game scheme is required to generate the classical game as a special case. Now, given a…
In recent years methods have been proposed to extend classical game theory into the quantum domain. This paper explores further extensions of these ideas that may have a substantial potential for further research. Upon reformulating quantum…
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…
Over the last twenty years of research on quantum game theory have given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing a 2x2 game introduced by J. Eisert, M.…
In this paper we provide a case study of the use of relatively sophisticated mathematics and algorithms to redefine and adapt a simple traditional game/puzzle to exploit the computational power of smart devices. The focus here is not so…