market platform designers

Abstract: We study worst-case VCG redistribution mechanism design for the public project problem, where n agents decide whether to build a non-excludable public project and the designer chooses a Groves term that returns as much of the VCG payment as possible without running a deficit. The objective is the worst-case efficiency ratio, the worst-case ratio between the agents' total utility and the first-best total utility. Prior work showed that this ratio can approach 1 as n grows only under a bounded precision assumption, that all types are rational numbers with a common bounded denominator. The assumption is stronger than it looks: it confines the difficult profiles to those in which all but a bounded number of agents report zero, and an agent who reports zero knows the total exactly. Without it, the best known guarantee tends to 1/2. We remove the assumption. We construct a deterministic, anonymous, strategy-proof, and non-deficit mechanism for arbitrary real types in [0,1] whose worst-case efficiency ratio is 1-O(1/log log n). The construction estimates the shortfall of the reported total below the project cost by filling in each agent's missing report with a resampled one, then estimates the error of that estimate, then the error of the error, and so on. After m rounds the aggregate error is at most 1/Hm mean reports, where Hm is the mth harmonic number. The proof of this bound is the heart of the paper and, unusually for a result about payments, uses complex analysis: a trigonometric representation of the shortfall function together with the Poisson-Jensen inequality for bounded analytic functions in the upper half plane.

Abstract: This paper investigates multi-agent reinforcement learning (MARL) in settings where firms compete for customers using congestible resources. We consider Bertrand competition in which firms compete by announcing prices and customers choose among firms based on both price and congestion. The relationship between price, congestion and the quantity of customers willing to accept service is governed by an unknown inverse demand curve, which firms must learn through experience. Each firm is modeled as a self-interested learning agent that chooses its price to maximize profit. A growing literature has shown that independently learning MARL agents can develop tacitly collusive behavior. We examine how such behavior emerges in markets with congestible resources. Our results provide insight into how learning dynamics, state representation, and strategic interaction jointly shape competition, with implications for both economic learning and the design of learning-enabled markets.