Formal Verification of Diffusion Auctions

TL;DR

This paper introduces a logical framework for formally verifying the strategic and dynamic aspects of diffusion auctions, enabling the analysis of equilibrium properties and seller strategies.

Contribution

It presents a novel logical formalism for diffusion auctions, along with model-checking procedures and complexity analysis, addressing a gap in formal verification and strategic reasoning.

Findings

Developed a logical formalism for diffusion and strategic behavior

Provided model-checking algorithms for Nash equilibrium verification

Established computational complexity results for the verification procedures

Abstract

In diffusion auctions, sellers can leverage an underlying social network to broaden participation, thereby increasing their potential revenue. Specifically, sellers can incentivise participants in their auction to diffuse information about the auction through the network. While numerous variants of such auctions have been recently studied in the literature, the formal verification and strategic reasoning perspectives have not been investigated yet. Our contribution is threefold. First, we introduce a logical formalism that captures the dynamics of diffusion and its strategic dimension. Second, for such a logic, we provide model-checking procedures that allow one to verify properties as the Nash equilibrium, and that pave the way towards checking the existence of sellers' strategies. Third, we establish computational complexity results for the presented algorithms.