Related papers: Nash equilibrium in quantum superpositions
This is a short review of the background and recent development in quantum game theory and its possible application in economics and finance. The intersection of science and society is also discussed. The review is addressed to…
Quantum games have attracted much attention in recent years due to their ability to solve decision-making dilemmas. The aim of this study is to extend previous work on quantum games by introducing a Mathematica package QEGS (Quantum…
In this paper we consider continuity of the set of Nash equilibria and approximate Nash equilibria for parameterized games. For parameterized games with unique Nash equilibria, the continuity of this equilibrium mapping is well-known.…
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. In this…
Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…
We build new quantum games, similar to the spin flip game, where as a novelty the players perform measurements on a quantum system associated to a continuous time search algorithm. The measurements collapse the wave function into one of the…
Effects of quantum and classical correlations on game theory are studied to clarify the new aspects brought into game theory by the quantum mechanical toolbox. In this study, we compare quantum correlation represented by a maximally…
The quest for understanding the complex phenomena of the world has led to the development of various fields of science, each with its own methods, models, and assumptions. However, sometimes these fields can intersect and inspire each…
A fundamental problem with the Nash equilibrium concept is the existence of certain "structurally deficient" equilibria that (i) lack fundamental robustness properties, and (ii) are difficult to analyze. The notion of a "regular" Nash…
We introduce a set-valued solution concept, M equilibrium, to capture empirical regularities from over half a century of game-theory experiments. We show M equilibrium serves as a meta theory for various models that hitherto were considered…
While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash…
We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are ``weakly'' stable: irrationality propagates and amplifies through players'…
We introduce Q-Nash, a quantum annealing algorithm for the NP-complete problem of Fnding pure Nash equilibria in graphical games. The algorithm consists of two phases. The first phase determines all combinations of best response strategies…
This work proposes a novel set of techniques for approximating a Nash equilibrium in a finite, normal-form game. It achieves this by constructing a new reformulation as solving a parameterized system of multivariate polynomials with tunable…
We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…
In this paper, we study a theoretical math problem of game theory and calculus of variations in which we minimize a functional involving two players. A general relationship between the optimal strategies for both players is presented,…
Graphon games are a class of games with a continuum of agents, introduced to approximate the strategic interactions in large network games. The first result of this study is an equilibrium existence theorem in graphon games, under the same…
In this short note we study a class of multi-player, turn-based games with deterministic state transitions and reachability / safety objectives (this class contains as special cases "classic" two-player reachability and safety games as well…
The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium.…
The two-players N strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme [1] are considered. It is shown that in the case of maximal entanglement no nontrivial pure Nash equilibrium exists. The proof relies on simple…