Polyhedral Clinching Auctions and the Adwords Polytope

TL;DR

This paper introduces a novel auction mechanism for polymatroidal environments that ensures incentive compatibility, individual rationality, and Pareto optimality while respecting budgets, with applications to AdWords and other markets.

Contribution

It presents a new clinching auction technique for polymatroidal constraints that simplifies previous methods and applies to multiple practical scenarios including AdWords auctions.

Findings

The auction mechanism is incentive compatible, individually rational, and Pareto optimal.

It applies to AdWords, bandwidth markets, and video on demand.

Extends previous results to new applications with polymatroidal constraints.

Abstract

A central issue in applying auction theory in practice is the problem of dealing with budget-constrained agents. A desirable goal in practice is to design incentive compatible, individually rational, and Pareto optimal auctions while respecting the budget constraints. Achieving this goal is particularly challenging in the presence of nontrivial combinatorial constraints over the set of feasible allocations. Toward this goal and motivated by AdWords auctions, we present an auction for {\em polymatroidal} environments satisfying the above properties. Our auction employs a novel clinching technique with a clean geometric description and only needs an oracle access to the submodular function defining the polymatroid. As a result, this auction not only simplifies and generalizes all previous results, it applies to several new applications including AdWords Auctions, bandwidth markets, and video on demand. In particular, our characterization of the AdWords auction as polymatroidal constraints might be of independent interest. This allows us to design the first mechanism for Ad Auctions taking into account simultaneously budgets, multiple keywords and multiple slots. We show that it is impossible to extend this result to generic polyhedral constraints. This also implies an impossibility result for multi-unit auctions with decreasing marginal utilities in the presence of budget constraints.