Decentralized Trading Networks: Equilibria and Fairness

TL;DR

This paper analyzes stability and fairness in decentralized trading networks, demonstrating convergence to equilibria and highlighting inherent fairness limitations for agents within core outcomes.

Contribution

It introduces new convergence results for dynamic trading models and reveals fundamental fairness constraints in core solutions.

Findings

Convergence to Nash and competitive equilibria is proven for dynamic trading models.

Essential agents can still receive zero utility in all core outcomes.

Inessential agents always receive zero utility in core outcomes.

Abstract

We explore stability and fairness considerations in decentralized networked markets with bilateral contracts, building on the trading networks framework [Hatfield et al., 2013]. In our trading network game, we show that a well-defined subset of Nash equilibria can be supported as competitive equilibria. Considering an offer-based trading dynamic as well as a stochastic price clock market, we prove new convergence results to Nash equilibrium and competitive equilibrium, providing a rationale for stability properties in decentralized, dynamic trading networks. Turning to the tension between fairness and (core) stability, we prove several negative results: inessential agents always receive zero utility in any core outcome, and even essential agents can get zero utility in all core outcomes.