Comparisons of standard royalty auctions with seller post-auction effort

Abstract

This study considers standard royalty auctions, in which each bidder’s valuation is determined endogenously by his type and the seller’s post-auction effort. We first characterize the unique symmetric separating D1 PBE of both sealed bid and ascending bid royalty auctions and compare them in terms of allocative efficiency, production efficiency, and seller revenue. We then show that no symmetric (semi-) pooling PBE survives the D1 criterion in these auctions (under mild conditions). Furthermore, we explore each bidder’s equilibrium bidding strategy, the associated efficiency and revenue, under a second-price royalty auction without disclosing the winning bid. We also consider a scenario where the seller adopts an entry fee instead of a reserve price to maximize their expected payoff. Finally, we examine the robustness of revenue ranking with respect to general forms of value creation.