Bipartiteness in Progressive Second-Price Multi-Auction Networks with Perfect Substitute

TL;DR

This paper analyzes decentralized bipartite markets with multiple PSP auctions, introducing a projection-based influence framework that explains auction dynamics, stability, and equilibrium formation without centralized control.

Contribution

It develops a novel influence framework for multi-auction PSP networks, formalizes influence sets, and models intra-round dynamics to explain market behavior and equilibrium stability.

Findings

Robustness of PSP auctions in decentralized settings

Structured phase transitions in multi-auction dynamics

Deterministic coverage of strategy space enabling stable equilibria

Abstract

We consider a bipartite network of buyers and sellers, where the sellers run locally independent Progressive Second-Price (PSP) auctions, and buyers may participate in multiple auctions, forming a multi-auction market with perfect substitute. The paper develops a projection-based influence framework for decentralized PSP auctions. We formalize primary and expanded influence sets using projections on the active bid index set and show how partial orders on bid prices govern allocation, market shifts, and the emergence of saturated one-hop shells. Our results highlight the robustness of PSP auctions in decentralized environments by introducing saturated components and a structured framework for phase transitions in multi-auction dynamics. This structure ensures deterministic coverage of the strategy space, enabling stable and truthful embedding in the larger game. We further model intra-round dynamics using an index to capture coordinated asynchronous seller updates coupled through buyers' joint constraints. Together, these constructions explain how local interactions propagate across auctions and gives premise for coherent equilibria--without requiring global information or centralized control.