Simple combinatorial auctions with budget constraints

Abstract

We study the efficiency of simple combinatorial auctions for the allocation of a set of items to a set of agents, with private subadditive valuation functions and budget constraints. e class we consider includes all auctions that allocate each item independently to the agent that submits the highest bid for it, and requests a payment that depends on the bids of all agents only for this item. Two well-known examples of this class are the simultaneous first and second price auctions. We focus on the pure equilibria of the induced strategic games, and using the liquid welfare as our efficiency benchmark, we show an upper bound of 2 on the price of anarchy for any auction in this class, as well as a tight corresponding lower bound on the price of stability for all auctions whose payment rules are convex combinations of the bids.is implies a tight bound of 2 on the price of stability of the well-known simultaneous first and second price auctions, which are members of the class. Additionally, we show lower bounds for the whole class, for more complex auctions (like VCG), and for se ings where the budgets are assumed to be common knowledge rather than private information.

Walrasian pricing in multi-unit auctions

“…There is a body of literature that considers envy-free pricing as a purely optimization problem (with no regard to incentives) and provides approximation algorithms and hardness results for maximizing revenue and welfare in different auction settings [8,32]. Incentives in auctions with budgets have also been considered [33,34,35] from the perspective of the Price of Anarchy [36] for the objective of the liquid welfare [4], a notion of the social welfare that incorporates the budgets into its definition, coined the "liquid price of Anarchy" in [33]. Again, these works study more general auction formats that multi-unit auctions, and without the envy-freeness constraint.…”

Multi-agent systems for computational economics and finance

“…Furthermore, we have analyzed the e ciency of auctions in se ings where the bidders have budget constraints that limit the amount of payments they can a ord. More speci cally, we have considered auctions for the allocation of divisible resources with bidders that have concave valuation functions for fractions of the resources [CV21], position auctions (including the GSP auction mentioned above) [Vou19], and simultaneous combinatorial auctions with payment rules that are convex combinations of the bids [Vou20].…”