相关论文: Non-Transitive Quantum Games

This article presents a unified probabilistic framework that allows both rational and irrational decision making to be theoretically investigated and simulated in classical and quantum games. Rational choice theory is a basic component of…

In this paper we quantize the Card Game. In the classical version of this game, one player (Alice) can always win with propability 2/3. But when the other player (Bob) is allowed to apply quantum strategy, the original unfair game turns…

Parrondo's Paradox arises when two losing games are combined to produce a winning one. A history dependent quantum Parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by…

In this research article, we survey existing quantum physics-related games and, based on this survey, propose a definition for the concept of quantum games. We define a quantum game as any type of rule-based game that either employs the…

Contextuality is arguably the fundamental property that makes quantum mechanics different from classical physics. It is responsible for quantum computational speedups in both magic-state-injection-based and measurement-based models of…

Stochastic games combine controllable and adversarial non-determinism with stochastic behavior and are a common tool in control, verification and synthesis of reactive systems facing uncertainty. Multi-objective stochastic games are natural…

The classic Rock-Paper-Scissors game of size 3 and its extension, Rock-Paper-Scissors-Lizard-Spock, are modeled by directed graphs called tournaments. They can be further extended to any odd size. The extended games are regular tournaments…

We study triples of labeled dice in which the relation "is a better die than" is non-transitive. Focusing on such triples with an additional symmetry we call "balance," we prove that such triples of $n$-sided dice exist for all $n \geq 3$.…

We study variations of classical combinatorial games on two finite heaps of tokens, a.k.a. \emph{subtraction games}. Given non-negative integers $p_1,q_1, p_2,q_2$, where $p_1q_2 > q_1p_2$, $p_1>0$ and $q_2>0$, two players alternate in…

We investigate quantum games in which the information is asymmetrically distributed among the players, and find the possibility of the quantum game outperforming its classical counterpart depends strongly on not only the entanglement, but…

This article examines mean-field-type game problems by means of a direct method. We provide various solvable examples beyond the classical linear-quadratic game problems. These include quadratic-quadratic games and games with power,…

In this work we propose and develop modified quantum games (zero and non-zero sum) in which payoffs and strategies are entangled. For the games studied, Nash and Pareto equilibriums are always obtained indicating that there are some…

We characterize all the pairs of complementary non-homogenous Beatty sequences $(A_n)_{n\ge 0}$ and $(B_n)_{n\ge 0}$ for which there exists an invariant game having exactly $\{(A_n,B_n)\mid n\ge 0\}\cup \{(B_n,A_n)\mid n\ge 0\}$ as set of…

An $n$-sided die is an $n$-tuple of positive integers. We say that a die $(a_1,\dots,a_n)$ beats a die $(b_1,\dots,b_n)$ if the number of pairs $(i,j)$ such that $a_i>b_j$ is greater than the number of pairs $(i,j)$ such that $a_i<b_j$. We…

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…

We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There…

Our preferences depend on the circumstances in which we reveal them. We will introduce a dependency which allows us to illustrate the relation between the possibility of winning of particular candidates in a quantum election and the type of…

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…

Bell inequality violation is the phenomenon where multiple non-communicating parties can exhibit correlations using quantum resources that are impossible if they can only use classical resources. One way to enforce non-communication is to…

We pursue the possible connections between classical games and quantum computation. The Parrondo game is one in which a random combination of two losing games produces a winning game. We introduce novel realizations of this Parrondo effect…