Optimistic-Conservative Bidding in Sequential Auctions

TL;DR

This paper analyzes sequential first-price auctions under optimistic conservative bidding, showing that such equilibria lead to minimal Walrasian outcomes and highlighting how bidding assumptions and sale order influence market results.

Contribution

It introduces optimistic conservative bidding in extensive form games and proves it results in minimal Walrasian equilibria in sequential auctions, contrasting with other equilibrium outcomes.

Findings

Optimistic conservative bidding leads to minimal Walrasian equilibrium.

Without conservative bidding, equilibria can predict high price of anarchy and low revenue.

Sale order impacts auction outcomes.

Abstract

In this work we consider selling items using a sequential first price auction mechanism. We generalize the assumption of conservative bidding to extensive form games (henceforth optimistic conservative bidding), and show that for both linear and unit demand valuations, the only pure subgame perfect equilibrium where buyers are bidding in an optimistic conservative manner is the minimal Walrasian equilibrium. In addition, we show examples where without the requirement of conservative bidding, subgame perfect equilibria can admit a variety of unlikely predictions, including high price of anarchy and low revenue in markets composed of additive bidders, equilibria which elicit all the surplus as revenue, and more. We also show that the order in which the items are sold can influence the outcome.