Combinatorial Auctions with Budgets

TL;DR

This paper introduces a polynomial-time, incentive-compatible auction mechanism for budget-constrained combinatorial auctions that guarantees Pareto-optimality, extending previous results to more complex auction settings.

Contribution

It presents a novel auction design that achieves incentive compatibility and Pareto-optimality in combinatorial auctions with private valuations and public budgets.

Findings

Auction runs in polynomial time.

Ensures incentive compatibility.

Guarantees Pareto-optimality.

Abstract

We consider budget constrained combinatorial auctions where bidder $i$ has a private value $v_i$, a budget $b_i$, and is interested in all the items in $S_i$. The value to agent $i$ of a set of items $R$ is $|R \cap S_i| \cdot v_i$. Such auctions capture adword auctions, where advertisers offer a bid for ads in response to an advertiser-dependent set of adwords, and advertisers have budgets. It is known that even of all items are identical and all budgets are public it is not possible to be truthful and efficient. Our main result is a novel auction that runs in polynomial time, is incentive compatible, and ensures Pareto-optimality for such auctions when the valuations are private and the budgets are public knowledge. This extends the result of Dobzinski et al. (FOCS 2008) for auctions of multiple {\sl identical} items and public budgets to single-valued {\sl combinatorial} auctions with public budgets.