Sequential Auctions and Externalities

TL;DR

This paper analyzes sequential auctions with externalities, revealing that auction order significantly impacts social welfare and demonstrating conditions under which efficiency and optimal outcomes are achieved or approximated.

Contribution

It introduces a novel analysis of sequential auctions with externalities, showing qualitative differences from simultaneous auctions and establishing equilibrium existence and efficiency results.

Findings

Sequential first-price auctions guarantee at least half of optimal welfare for unit-demand bidders.

Second-price and submodular bidders can have arbitrarily low welfare compared to optimal.

Sequential matroid auctions always implement the VCG outcome and are efficient.

Abstract

In many settings agents participate in multiple different auctions that are not necessarily implemented simultaneously. Future opportunities affect strategic considerations of the players in each auction, introducing externalities. Motivated by this consideration, we study a setting of a market of buyers and sellers, where each seller holds one item, bidders have combinatorial valuations and sellers hold item auctions sequentially. Our results are qualitatively different from those of simultaneous auctions, proving that simultaneity is a crucial aspect of previous work. We prove that if sellers hold sequential first price auctions then for unit-demand bidders (matching market) every subgame perfect equilibrium achieves at least half of the optimal social welfare, while for submodular bidders or when second price auctions are used, the social welfare can be arbitrarily worse than the optimal. We also show that a first price sequential auction for buying or selling a base of a matroid is always efficient, and implements the VCG outcome. An important tool in our analysis is studying first and second price auctions with externalities (bidders have valuations for each possible winner outcome), which can be of independent interest. We show that a Pure Nash Equilibrium always exists in a first price auction with externalities.