mars 2026

Date: 20/03/2026 à 11h30 Lieu: Salle C057 Titre: Learning in Proportional Allocation Auctions Games Résumé : The Kelly or proportional allocation mechanism is a simple and efficient auction-based scheme that distributes an infinitely divisible resource proportionally to the agents’ bids. When agents are aware of the allocation rule, their interactions form a game, that has been extensively studied. This paper examines the less explored repeated Kelly game, focusing mainly on utilities that are logarithmic in the allocated resource fraction. We first derive this logarithmic form from fairness–throughput trade-offs in wireless network slicing, and then prove that the induced stage game admits a unique Nash equilibrium (NE). For the repeated play, we prove convergence to this NE under three behavioral models: (i) all agents use Online Gradient Descent (OGD), (ii) all agents use Dual Averaging with a quadratic regularizer (DAQ) (a variant of the Follow-the-Regularized leader algorithm), and (iii) all agents play myopic best responses (BR). Our convergence results hold even when agents use personalized learning rates in OGD and DAQ (e.g., tuned to optimize individual regret bounds), and they extend to a broader class of utilities that meet a certain sufficient condition. Finally, we complement our theoretical results with extensive Plus d'infos