Related papers: Permissible four-strategy quantum extensions of cl…
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…
Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…
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 propose a scheme for a quantum game based on performing an EPR type experiment and in which each player's spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting 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 modify the concept of quantum strategic game to make it useful for extensive form games. We prove that our modification allows to consider the normal representation of any finite extensive game using the fundamental concepts of quantum…
The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the…
Research in quantum games has flourished during recent years. However, it seems that opinion remains divided about their true quantum character and content. For example, one argument says that quantum games are nothing but 'disguised'…
A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given. Decoherence in other types of quantum games is…
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…
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…
We study the advantages of quantum strategies in evolutionary social dilemmas on evolving random networks. We focus our study on the two-player games: prisoner's dilemma, snowdrift and stag-hunt games. The obtained result show the benefits…
A model of a quantum version of classical games should reproduce the original classical games in order to be able to make a comparative analysis of quantum and classical effects. We analyze a class of symmetric multipartite entangled states…
We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…
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…
The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…
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 investigate quantum strategy in moving frames by considering Prisoner's Dilemma and propose four thresholds of $\gamma$ for two players to determine their \textit{Nash Equilibria}. Specially, an interesting phenomenon appears in…
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…
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…