Related papers: Quantum mean field games
Mean field game theory studies the behavior of a large number of interacting individuals in a game theoretic setting and has received a lot of attention in the past decade (Lasry and Lions, Japanese journal of mathematics, 2007). In this…
This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…
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…
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…
The fundamental laws of quantum world upsets the logical foundation of classic physics. They are completely counter-intuitive with many bizarre behaviors. However, this paper shows that they may make sense from the perspective of a general…
Mean field games (MFGs) tractably model behavior in large agent populations. The literature on learning MFG equilibria typically focuses on finding Nash equilibria (NE), which assume perfectly rational agents and are hence implausible in…
An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint…
The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…
Quantum phenomena have remained largely inaccessible to the general public. This can be attributed to the fact that we do not experience quantum mechanics on a tangible level in our daily lives. Games can provide an environment in which…
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…
We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. In generative flows, a Lagrangian formulation is used where each particle (generated sample)…
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…
We develop a rigorous mathematical framework for quantum game theory applied to static 2x2 games, extending classical concepts to the quantum setting where players may employ arbitrary unitary operations (pure strategies) or probability…
Mean field games were introduced independently by J-M. Lasry and P-L. Lions, and by M. Huang, R.P. Malham\'e and P. E. Caines, in order to bring a new approach to optimization problems with a large number of interacting agents. The…
This compendium features advances in Game Theory, to include: Classical Game Theory: Cooperative and non-cooperative. Zero-sum and non-zero sum games. Potential and Congestion games. Mean Field games. Nash Equilibrium, Correlated Nash…
The mean field games (MFG) paradigm was introduced to provide tractable approximations of games involving very large populations. The theory typically rests on two key assumptions: homogeneity, meaning that all players share the same…
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…
We give a concise and self-contained introduction to the theory of Quantum Games by reviewing the seminal works of Meyer, Eisert-Wilkens-Lewenstein, Marinatto-Weber and Landsburg, which initiated the study of this field. By generalizing…
Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…
This paper studies Mean Field Games (MFGs) in which agent dynamics are given by jump processes of controlled intensity, with mean-field interaction via the controls and affecting the jump intensities. We establish the existence of MFG…