Statistical mechanics of budget-constrained auctions

Statistical mechanics of budget-constrained auctions

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). Based on the cavity method of statistical mechanics, we introduce a message passing algorithm that is c...

Statistical mechanics of combinatorial auctions.

Combinatorial auctions are formulated as frustrated lattice gases on sparse random graphs, allowing the determination of the optimal revenue by methods of statistical physics. Transitions between computationally easy and hard regimes are found and interpreted in terms of the geometric structure of the space of solutions. We introduce an iterative algorithm to solve intermediate and large instan...

Keyword Auctions with Budget-constrained Bidders

We study a keyword auction model where bidders have constrained budgets. In the absence of budget constraints, Edelman, Ostrovsky, and Schwarz (2007) and Varian (2007) analyze “locally envy-free equilibrium” or “symmetric Nash equilibrium” bidding strategies in generalized second-price (GSP) auctions. However, bidders often have to set their daily budgets when they participate in an auction; on...

Approximation Algorithms for Budget-Constrained Auctions

Multiple-Object Auctions with Budget Constrained Bidders

A seller with two objects faces a group of bidders who are subject to budget constraints. The objects have common values to all bidders, but need not be identical and may be either complements or substitutes. In a simple complete information setting we show: (1) if the objects are sold by means of a sequence of open ascending auctions, then it is always optimal to sell the more valuable object ...