Auctions with a Profit Sharing Contract

TL;DR

This paper analyzes how profit sharing contracts in auctions can increase seller revenue by sharing profits and losses, outperforming traditional one-time payment auctions in various settings.

Contribution

It demonstrates that profit sharing contracts, including sharing losses, can significantly enhance auction revenue beyond traditional payment schemes.

Findings

Profit sharing contracts increase expected revenue in second price and English auctions.

Sharing both profits and losses yields higher revenue than sharing profits alone.

General classes of profit sharing contracts outperform one-time payments in revenue generation.

Abstract

We study the problem of selling a resource through an auction mechanism. The winning buyer in turn develops this resource to generate profit. Two forms of payment are considered: charging the winning buyer a one-time payment, or an initial payment plus a profit sharing contract (PSC). We consider a symmetric interdependent values model with risk averse or risk neutral buyers and a risk neutral seller. For the second price auction and the English auction, we show that the seller's expected total revenue from the auction where he also takes a fraction of the positive profit is higher than the expected revenue from the auction with only a one-time payment. Moreover, the seller can generate an even higher expected total revenue if, in addition to taking a fraction of the positive profit, he also takes the same fraction of any loss incurred from developing the resource. Moving beyond simple PSCs, we show that the auction with a PSC from a very general class generates higher expected total revenue than the auction with only a one-time payment. Finally, we show that suitable PSCs provide higher expected total revenue than a one-time payment even when the incentives of the winning buyer to develop the resource must be addressed by the seller.