Scoring Auctions with Coarse Beliefs

TL;DR

This paper introduces a framework for analyzing scoring auctions where agents have coarse, uncertain beliefs, providing a full classification of auction types based on their strategic complexity and information requirements.

Contribution

It develops a model of prior-free, coarse belief equilibria in scoring auctions and characterizes the conditions under which auctions are strategically simple or complex.

Findings

Classifies auctions into two categories based on information learning requirements.

Provides a primitive condition to distinguish between simple and complex scoring auctions.

Categorizes real-world scoring auctions by their strategic simplicity.

Abstract

This paper studies a simplicity notion in a mechanism design setting in which agents do not necessarily share a common prior. I develop a model in which agents participate in a prior-free game of (coarse) information acquisition followed by an auction. After acquiring information, the agents have uncertainty about the environment in which they play and about their opponents' higher-order beliefs. A mechanism admits a coarse beliefs equilibrium if agents can play best responses even with this uncertainty. Focusing on multidimensional scoring auctions, I fully characterize a property that allows an auction format to admit coarse beliefs equilibria. The main result classifies auctions into two sets: those in which agents learn relatively little about their setting versus those in which they must fully learn a type distribution to form equilibrium strategies. I then find a simple, primitive condition on the auction's rules to distinguish between these two classes. I then use the condition to categorize real-world scoring auctions by their strategic simplicity.