Strategyproofness and Monotone Allocation of Auction in Social Networks

TL;DR

This paper introduces a new framework for strategyproof network auctions by classifying monotone allocation rules into ID-MON and IP-MON, providing conditions for strategyproof payments and resolving key challenges in combinatorial network auctions.

Contribution

It identifies two fundamental categories of monotone allocation rules in social network auctions and characterizes strategyproof payment rules for them, addressing a major gap in the field.

Findings

All existing network auction rules are encompassed by ID-MON and IP-MON categories.

Conditions for the existence of strategyproof payment rules are characterized.

The revenue-maximizing strategyproof payment rule is shown to be computationally feasible.

Abstract

Strategyproofness in network auctions requires that bidders not only report their valuations truthfully, but also do their best to invite neighbours from the social network. In contrast to canonical auctions, where the value-monotone allocation in Myerson's Lemma is a cornerstone, a general principle of allocation rules for strategyproof network auctions is still missing. We show that, due to the absence of such a principle, even extensions to multi-unit network auctions with single-unit demand present unexpected difficulties, and all pioneering researches fail to be strategyproof. For the first time in this field, we identify two categories of monotone allocation rules on networks: Invitation-Depressed Monotonicity (ID-MON) and Invitation-Promoted Monotonicity (IP-MON). They encompass all existing allocation rules of network auctions as specific instances. For any given ID-MON or IP-MON allocation rule, we characterize the existence and sufficient conditions for the strategyproof payment rules, and show that among all such payment rules, the revenue-maximizing one exists and is computationally feasible. With these results, the obstacle of combinatorial network auction with single-minded bidders is now resolved.