Related papers: Quantum strategies and evolutionary stability (in …
We give a mathematical definition of dynamical evolution in quantum field theory, including evolution on space-like surfaces, and show its relationship with the axiomatic and perturbative approaches to QFT.
Rules of quantization and equations of motion for a finite-dimensional formulation of Quantum Field Theory are proposed which fulfill the following properties: a) both the rules of quantization and the equations of motion are covariant; b)…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
We introduce and investigate a range of general notions of a game. Our principal notion is based on a set of agents modifying a relational structure in a discrete evolution sequence. We also introduce and study a variety of ways to model…
Methods of exploring Nash equilibrium in quantum games are studied. Analytical conditions of the existence, the uniqueness or the multiplicity of the equilibria are found.
Recently, a standardized framework was proposed for introducing quantum-inspired moves in mathematical games with perfect information and no chance. The beauty of quantum games-succinct in representation, rich in structures, explosive in…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
We present a concise but complete conceptual treatment of quantum computing implemented with Cavity Quantum Electrodynamics (CQED. The paper is intended as a brief overview for professionals who are coming over to the field from other areas…
This paper presents a new mathematical formalism that describes the quantization of games. The study of so-called quantum games is quite new, arising from a seminal paper of D. Meyer \cite{Meyer} published in Physics Review Letters in 1999.…
Evolutionary game theory is an abstract and simple, but very powerful way to model evolutionary dynamics. Even complex biological phenomena can sometimes be abstracted to simple two-player games. But often, the interaction between several…
An encyclopedia article on mathematical aspects of quantum field theory in curved spacetime. Section titles are: Introduction and preliminaries; Construction of *-algebra for a real linear scalar field on globally hyperbolic spacetimes and…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the…
We examine the classical contents of quantum games. It is shown that a quantum strategy can be interpreted as a classical strategies with effective density-dependent game matrices composed of transposed matrix elements. In particular,…
I draw attention to statistical, probabilistic, computer science aspects of the highly related topics of the Bell game and of a possible future Quantum Internet.
This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the…
We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence.…
The multi-population replicator dynamics (RD) can be considered a dynamic approach to the study of multi-player games, where it was shown to be related to Cross' learning, as well as of systems of coevolving populations. However, not all of…
Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented…
Recent years have seen noteworthy progress in the mathematical formulation of quantum field theory and perturbative string theory. We give a brief survey of these developments. It serves as an introduction to the more detailed collection…