Search results for "Stochastic"
showing 10 items of 1018 documents
A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma
2016
We study diffusion of cooperation in a two-population game in continuous time. At each instant, the game involves two random individuals, one from each population. The game has the structure of a Prisoner's dilemma where each player can choose either to cooperate (c) or to defect (d), and is reframed within the field of approachability in two-player repeated game with vector payoffs. We turn the game into a dynamical system, which is positive, and propose a saturated strategy that ensures local asymptotic stability of the equilibrium (c, c) for any possible choice of the payoff matrix. We show that there exists a rectangle, in the space of payoffs, which is positively invariant for the syst…
Consensus in opinion dynamics as a repeated game
2018
Abstract We study an n -agent averaging process with dynamics subject to controls and adversarial disturbances. The model arises in multi-population opinion dynamics with macroscopic and microscopic intertwined dynamics. The averaging process describes the influence from neighbouring populations, whereas the input term indicates how the distribution of opinions in the population changes as a result of dynamical evolutions at a microscopic level (individuals’ changing opinions). The input term is obtained as the vector payoff of a two player repeated game. We study conditions under which the agents achieve robust consensus to some predefined target set. Such conditions build upon the approac…
The shape of small sample biases in pricing kernel estimations
2016
AbstractNumerous empirical studies find pricing kernels that are not-monotonically decreasing; the findings are at odds with the pricing kernel being marginal utility of a risk-averse, so-called representative agent. We study in detail the common procedure which estimates the pricing kernel as the ratio of two separate density estimations. In the first step, we analyse theoretically the functional dependence for the ratio of a density to its estimated density; this cautions the reader regarding potential computational issues coupled with statistical techniques. In the second step, we study this quantitatively; we show that small sample biases shape the estimated pricing kernel, and that est…
Market reaction to a bid-ask spread change: a power-law relaxation dynamics.
2009
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of price…
Local regularity for time-dependent tug-of-war games with varying probabilities
2016
We study local regularity properties of value functions of time-dependent tug-of-war games. For games with constant probabilities we get local Lipschitz continuity. For more general games with probabilities depending on space and time we obtain H\"older and Harnack estimates. The games have a connection to the normalized $p(x,t)$-parabolic equation $(n+p(x,t))u_t=\Delta u+(p(x,t)-2) \Delta_{\infty}^N u$.
Population Games with Vector Payoff and Approachability
2016
This paper studies population games with vector payoffs. It provides a new perspective on approachability based on mean-field game theory. The model involves a Hamilton-Jacobi-Bellman equation which describes the best-response of every player given the population distribution and an advection equation, capturing the macroscopic evolution of average payoffs if every player plays its best response.
ORGANIZED LEARNING MODELS (PURSUER CONTROL OPTIMISATION)
1983
Abstract The concept of Organized Learning is defined, and some random models are presented. For Not Transferable Learning, it is necessary to start from an instantaneous learning; by a discrete way, we must form a stochastic model considering the probability of each path; with a continue aproximation, we can study the evolution of the internal state through to consider the relative and absolute probabilities, by means of differential equations systems. For Transferable Learning, the instantaneous learning give us directly the System evolution. So, the Algoritmes for the different models are compared.
Average Performance Analysis of the Stochastic Gradient Method for Online PCA
2019
International audience; This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting. We also propose an online approach for selecting the learning rate. Simulation experiments confirm the practical relevance of the plain stochastic gradient approach and that drastic improvements can be achieved by learning the learning rate.
Theory of Heterogeneous Circuits With Stochastic Memristive Devices
2022
We introduce an approach based on the Chapman-Kolmogorov equation to model heterogeneous stochastic circuits, namely, the circuits combining binary or multi-state stochastic memristive devices and continuum reactive components (capacitors and/or inductors). Such circuits are described in terms of occupation probabilities of memristive states that are functions of reactive variables. As an illustrative example, the series circuit of a binary memristor and capacitor is considered in detail. Some analytical solutions are found. Our work offers a novel analytical/numerical tool for modeling complex stochastic networks, which may find a broad range of applications.
Modelling of non-stationary mobile radio channels using two-dimensional brownian motion processes
2013
The interdisciplinary idea of this paper is to employ a two-dimensional (2D) Brownian motion (BM) process to model non-stationary mobile fading channels. It is assumed that the mobile station (MS) starts moving from a fixed point along a random path in the 2D plane. We model such a moving scenario by a 2D BM process, in which the variance of the process determines the deviation of the MS from its starting point. The propagation area is modelled by a non-centred one-ring scattering model, where the local scatterers are uniformly distributed on a ring centred not necessarily on the MS. The random movement of the MS in the proposed scattering model results in local angles-of-arrival (AOAs) and…