arXiv subjects

Olivier Gallay

Publications and source records attributed to Olivier Gallay.

7 recordsLinked to original sources

arXiv2024

Nonlinear Economic State Equilibria via van der Waals Modeling

The renowned van der Waals (VDW) state equation quantifies the equilibrium relationship between pressure $P$, volume $V$ and temperature $k_{B}T$ of a real gas. We assign new variable interpretations adapted to the economic context: $P \rightarrow Y$, representing price; $V \rightarrow X$, representing demand; and $k_{B}T \rightarrow κ$, representing income, to describe an economic state equilibrium. With this reinterpretation, the price elasticity of demand (PED) and the income elasticity of demand (YED) are non-constant factors and may exhibit a singularity of the cusp-catastrophe type. Within this economic framework, the counterpart of VDW liquid-gas phase transition illustrates a substitution mechanism where one product or service is replaced by an alternative substitute. The conceptual relevance of this reinterpretation is discussed qualitatively and quantitatively via several illustrations ranging from transport (carpooling), medical context (generic versus original medication) and empirical data drawn from the electricity market in Germany.

nlin.AO↗

arXiv2023

Stochastic Pairwise Preference Convergence in Bayesian Agents

Beliefs inform the behavior of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to explain how preferences evolve in cases of simple agent interactions. In this paper, we derive a Gaussian, pairwise agent interaction model to study how preferences converge when driven by observation of each other's behaviors. We show that the dynamics of convergence resemble an Ornstein-Uhlenbeck process, a common model in nonequilibrium stochastic dynamics. Using standard analytical and computational techniques, we find that the hyperprior magnitudes, representing the learning time, determine the convergence value and the asymptotic entropy of the preferences across pairs of agents. We also show that the dynamical variance in preferences is characterized by a relaxation time $t^\star$, and compute its asymptotic upper bound. This formulation enhances the existing toolkit for modeling stochastic, interactive agents by formalizing leading theories in learning theory, and builds towards more comprehensive models of open problems in principal-agent and market theory.

nlin.AO↗

arXiv2019

Intraday Retail Sales Forecast: An Efficient Algorithm for Quantile Additive Modeling

With the ever increasing prominence of data in retail operations, sales forecasting has become an essential pillar in the efficient management of inventories. When facing high demand, the use of backroom storage and intraday shelf replenishment is necessary to avoid stock-out. In that context, the mandatory input for any successful replenishment policy to be implemented is access to reliable forecasts for the sales at an intraday granularity. To that end, we use quantile regression to adapt different patterns from one product to the other, and we develop a stable and efficient quantile additive model algorithm to compute sales forecasts in an intradaily context. Our algorithm is computationally fast and is therefore suitable for use in real-time dynamic shelf replenishment. As an illustration, we examine the case of a highly frequented store, where the demand for various alimentary products is accurately estimated over the day with the help of the proposed algorithm.

stat.AP↗

arXiv2019

Imitation, proximity, and growth -- A collective swarm dynamics approach

This paper is based on the premise that economic growth is driven by an interplay between innovation and imitation in an economy composed of interacting firms operating in a stochastic environment. A novel approach to modeling imitation is presented, based on range-dependent processes that describe how firms consider proximity when imitating peers who are found in a given neighborhood in terms of productivity. Using a particularly tractable approach, we are able to analyze how drastically different economic growth scenarios emerge from different imitation strategies. These emerging scenarios range from diffusive growth where the variance of productivity grows indefinitely, to balanced growth described by a traveling wave with fixed variance. The latter scenario is sustained only when imitation strength among firms exceeds a critical bifurcation threshold.

nlin.PS↗

arXiv2019

Opinion formation dynamics -- Swift collective disillusionment triggered by unmet expectations

We propose a microscopic model to describe how individual opinions shared between interacting agents initiate excessive collective expectations about a new idea or an innovation, followed by a swift collapse towards a dramatic collective disillusionment. The basic assumption which underlies the dynamics is that the information gathering process is not instantaneous but requires maturation. Agents steadily refine and update their personal opinion via a recurrent consultation of a public pool which stores information tokens (ITs). The expectation for the innovative idea is monitored in real-time by counting the number of stored ITs. The flow dynamics of ITs is assimilated to a single node queuing system (QS) with feedback loop. It incorporates the information pool (the waiting room), an IT inflow, and a service outflow that stylizes the information gathering process. Contrary to basic queuing theory, here the ITs roaming the QS are endowed with time-dependent internal variables. This additional dynamic information is used to construct the information maturation process. Such a maturation of the information introduces response delays into the dynamics, which ultimately generates the collective disillusionment trough. We illustrate the introduced generic modeling framework by considering in details the hype cycle dynamics, a key managerial topic when dealing with diffusion of innovation. In a second part of the paper, we introduce a stylized framework to detect, as soon as possible, the onset of the collective disillusionment phase, while minimizing the frequency of false alarms.

nlin.AO↗

arXiv2012

Co-evolving agents subject to local versus nonlocal barycentric interactions

The mean-field dynamics of a collection of stochastic agents with local versus nonlocal interactions is studied via analytically soluble models. The nonlocal interactions result from a barycentric modulation of the observation range of the agents. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.

nlin.AO↗

arXiv2011

Spatio-Temporal Patterns for a Generalized Innovation Diffusion Model

We construct a model of innovation diffusion that incorporates a spatial component into a classical imitation-innovation dynamics first introduced by F. Bass. Relevant for situations where the imitation process explicitly depends on the spatial proximity between agents, the resulting nonlinear field dynamics is exactly solvable. As expected for nonlinear collective dynamics, the imitation mechanism generates spatio-temporal patterns, possessing here the remarkable feature that they can be explicitly and analytically discussed. The simplicity of the model, its intimate connection with the original Bass' modeling framework and the exact transient solutions offer a rather unique theoretical stylized framework to describe how innovation jointly develops in space and time.

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