arXiv subjects

Yann Kerzreho

Publications and source records attributed to Yann Kerzreho.

3 recordsLinked to original sources

arXiv2026

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation

We study horizontal differentiation when the set of feasible products is a structured subset of the Lancasterian characteristics space. Modeling this set as a compact Riemannian manifold, we show that intrinsic geometry governs substitutability and thereby determines market outcomes. We establish that production constraints induce sectional curvature, which controls the elasticity of technological substitution. Negative curvature amplifies technological divergence and attenuates competitive pressure, whereas positive curvature compresses technological distances and intensifies competition. This mapping yields a characterization of spatial competition in which equilibrium existence and stability are determined by geometric primitives. In particular, we show that sufficiently negative curvature and high dimensionality stabilize minimum differentiation, while continuous symmetries preclude it. The analysis provides a microfoundation linking technological constraints, through the geometry of the feasible set, to endogenous regimes of market power.

q-fin.MF↗

arXiv2025

Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games

This paper introduces a new approach for approximating the learning dynamics of multiple reinforcement learning (RL) agents interacting in a finite-state Markov game. The idea is to rescale the learning process by simultaneously reducing the learning rate and increasing the update frequency, effectively treating the agent's parameters as a slow-evolving variable influenced by the fast-mixing game state. Under mild assumptions-ergodicity of the state process and continuity of the updates-we prove the convergence of this rescaled process to an ordinary differential equation (ODE). This ODE provides a tractable, deterministic approximation of the agent's learning dynamics. An implementation of the framework is available at\,: https://github.com/yannKerzreho/MarkovGameApproximation

stat.ML↗

arXiv2024

Generating social networks with static and dynamic utility-maximization approaches

In this paper, we introduce a conceptual framework that model human social networks as an undirected dot-product graph of independent individuals. Their relationships are only determined by a cost-benefit analysis, i.e. by maximizing an objective function at the scale of the individual or of the whole network. On this framework, we build a new artificial network generator in two versions. The first fits within the tradition of artificial network generators by being able to generate similar networks from empirical data. The second relaxes the computational efficiency constraint and implements the same micro-based decision algorithm, but in agent-based simulations with time and fully independent agents. This latter version enables social scientists to perform an in-depth analysis of the consequences of behavioral constraints affecting individuals on the network they form. This point is illustrated by a case study of imperfect information.

math.PR↗