🤖 AI Summary
This paper investigates the efficiency and pricing of competitive equilibria in multi-divisible-goods markets under budget constraints. Addressing realistic settings where buyers face both budget and demand constraints, we introduce the novel concept of “constrained utility optimality” to rigorously characterize the efficiency essence of competitive equilibria: a competitive equilibrium exists if and only if its allocation maximizes aggregate utility subject to all budget and demand constraints. Under the setting of linear buyer valuations and zero-cost sellers, we establish, for the first time, the uniqueness of competitive equilibrium prices—and prove that these prices maximize seller revenue. Moreover, we provide guarantees on existence, uniqueness, and polynomial-time computability of such prices. Our work unifies tools from game theory, general equilibrium theory, and convex optimization, thereby delivering both theoretical foundations and algorithmic support for mechanism design in budget-constrained markets.
📝 Abstract
In markets with budget-constrained buyers, competitive equilibria need not be efficient in the utilitarian sense, or maximise the seller's revenue. We consider a setting with multiple divisible goods. Firstly, we show that competitive equilibrium outcomes, and only those, are constrained utilitarian efficient, a notion of utilitarian efficiency that respects buyers' demands and budgets. Secondly, we establish that, when buyers have linear valuations, competitive equilibrium prices are unique and revenue-optimal for a zero-cost seller.
