Related papers: Game-theoretic Brownian motion
Brownian motion whose infinitesimal variance changes according to a three-state continuous time Markov Chain is studied. This Markov Chain can be viewed as a telegraph process with one on state and two off states. We first derive the…
By studying a system of Brownian particles, interacting only through a local social-like force (velocity alignment), we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped…
In systems possessing a spatial or dynamical symmetry breaking thermal Brownian motion combined with unbiased, non-equilibrium noise gives rise to a channelling of chance that can be used to exercise control over systems at the micro- and…
A communication game consists of distributed parties attempting to jointly complete a task with restricted communication. Such games are useful tools for studying limitations of physical theories. A theory exhibits preparation contextuality…
In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…
We provide some examples showing how game-theoretic arguments can be used in computability theory and algorithmic information theory: unique numbering theorem (Friedberg), the gap between conditional complexity and total conditional…
There are only limited classes of multi-player stochastic games in which independent learning is guaranteed to converge to a Nash equilibrium. Markov potential games are a key example of such classes. Prior work has outlined sets of…
The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical…
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…
Optimal behavior in (competitive) situation is traditionally determined with the help of utility functions that measure the payoff of different actions. Given an ordering on the space of revenues (payoffs), the classical axiomatic approach…
A study of the non-dissipative Brownian motion in vacuum is presented. The noise source associated to the stochastic process assumed in this work is vacuum fluctuations of some quantum field capable of interact with a massive particle. For…
We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at $-\infty$. We show that these processes do not have to have…
In this article, we study the potential theory of normal tempered stable process which is obtained by time-changing the Brownian motion with a tempered stable subordinator. Precisely, we study the asymptotic behavior of potential density…
A general theory of stochastic decision forests is developed to bridge two concepts of information flow: decision trees and refined partitions on the one side, filtrations from probability theory on the other. Instead of the traditional…
Two losing games, when alternated in a periodic or random fashion, can produce a winning game. This paradox occurs in a family of stochastic processes: if one combines two or more dynamics where a given quantity decreases, the result can be…
This paper derives a complete analytical solution for the probability distribution of the configuration of a non-holonomic vehicle that moves in two spatial dimensions by satisfying the unicycle kinematic constraints and in presence of…
We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the…
Stochastic Schr\"odinger equations that govern the dynamics of open quantum systems are given by the equations for signal processing. In particular, the Brownian motion that drives the wave function of the system does not represent noise,…
We investigate the increasingly important and common game-solving setting where we do not have an explicit description of the game but only oracle access to it through gameplay, such as in financial or military simulations and computer…