arXiv subjects

Ali Ellouze

Publications and source records attributed to Ali Ellouze.

3 recordsLinked to original sources

arXiv2025

Convergence to stationary points in the Weisbuch-Kirman-Herreiner model for buyers' preferences in fish markets

In a paper published in The Economic Journal in 2000, Weisbuch et al.\ introduce a model for buyers' preferences to the various sellers in over-the-counter (OTC) fish markets. While this model has become an archetype of economic conceptualization that combines bounded rationality and myopic reasoning, the literature on its asymptotic behaviours has remained scarce. In this paper, we proceed to a mathematical analysis of the dynamics and its full characterization in the simplest case of homogeneous buyer populations. By using elements of the theory of cooperative dynamical systems, we prove that, independently of the number of sellers and parameters, for almost every initial condition, the subsequent trajectory must asymptotically approach a stationary state. Moreover, for simple enough distributions of the sellers' attractiveness, we determine all stationary states and their parameter-dependent stability. This analysis shows that in most cases, the asymptotic preferences are ordered as the attractiveness are. However, depending on the parameters, there also exist robust functioning modes in which those sellers with highest preference are not the ones that provide highest profit.

econ.TH↗

arXiv2025

A simple model for the population dynamics in OTC wholesale fresh product markets

Given the combined evidences of bounded rationality, limited information and short-term optimization, over-the-counter (OTC) fresh product markets provide a perfect instance where to develop a behavioural approach to the analysis of micro-economic systems. Aiming at characterizing via a rigorous mathematical analysis, the main features of the spontaneous organization and functioning of such markets, we introduce and we study a stylized dynamical model for the time evolution of buyers populations and prices/attractiveness at each wholesaler. The dynamics is governed by immediate reactions of the actors to changes in basic indicators. Buyers are influenced by some degree of loyalty to their regular suppliers. Yet, at times, they also prospect for potential better offers. On the other hand, sellers primarily aim at maximising their profit. Yet, they can be also prone to improving their competitiveness in case of clientele deficit. Our results reveal that, in spite of being governed by simple and immediate rules, the competition between sellers self-regulates in time, as it constrains to bounded ranges the dispersion of both prices and clientele volumes, does similarly for the mean clientele volume, and it generates oscillatory behaviours that prevent any seller to dominate permanently its competitors (and to be dominated forever). Long-term behaviours are also investigated, with focus on asymptotic convergence to an equilibrium, as can be expected for a standard functioning mode. In particular, in the simplest case of 2 competing sellers, a normal-form-like analysis proves that such convergence holds, provided that the buyer's loyalty is sufficiently high or the sellers' reactivity is sufficiently low. In other words, this result identifies and proves those characteristics of the system that are responsible for long term stability and asymptotic damping of the oscillations.

econ.TH↗

arXiv2023

Dynamics of buyer populations in fresh product markets

Based on empirical evidences and previous studies, we introduce and mathematically study a perception-driven model for the dynamics of buyer populations in markets of perishable goods. Buyer behaviours are driven partly by some loyalty to the sellers that they previously purchased at, and partly by the sensitivity to the intrinsic attractiveness of each seller in the market. On the other hand, the sellers update they attractiveness in time according to the difference between the volume of their clientele and the mean volume of buyers in the market, optimising either their profit when this difference is favourable or their competitiveness otherwise. While this negative feedback mechanism is a source of instability that promotes oscillatory behaviour, our analysis identifies the critical features of the dynamics that are responsible for the asymptotic stability of the stationary states, both in their immediate neighbourhood and globally in phase space. Altogether, this study provides mathematical insights into the consequences of introducing feedback into buyer-seller interactions in such markets, with emphasis on identifying conditions for long term constancy of clientele volumes.

econ.TH↗