Strategyproofness and Monotone Allocation of Auction in Social Networks

2025-07-19

AI Summary

Existing allocation mechanisms in social network auctions struggle to simultaneously achieve strategy-proofness and revenue optimization, particularly in multi-unit and combinatorial settings where strategic manipulation via invitation is prevalent. Method: We introduce two novel network monotonicity conditions—Invitation-Diminishing Monotonicity (ID-MON) and Invitation-Promoting Monotonicity (IP-MON)—to uniformly characterize incentive-compatible allocations in social networks. We establish their necessary and sufficient connection to strategy-proof payment rules and derive a computationally tractable, revenue-maximizing payment scheme grounded in mechanism design principles and network topology constraints. Contribution/Results: Our framework overcomes fundamental limitations of classical auction theory by achieving, for the first time, simultaneous incentive compatibility and revenue optimality in single-demand multi-item auctions and single-dimensional combinatorial auctions on social networks. It provides a general, scalable foundation for mechanism design in networked environments.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Social mining and social search on the Web
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Lack of general allocation principles for strategyproof network auctions
• Difficulties in extending to multi-unit network auctions
• Identifying monotone allocation rules for strategyproof payment conditions

Innovation

• Introduces ID-MON and IP-MON allocation rules
• Characterizes strategyproof payment rules conditions
• Ensures revenue-maximizing payment feasibility