Decentralized Trading Networks: Equilibria and Fairness

TL;DR

In this trading network game, it is shown that a well-defined subset of Nash equilibria can be supported as competitive equilibria, providing a rationale for stability properties in decentralized, dynamic trading networks.

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.

Figures (8)

• Figure 1: A two-agent trading network, associated valuations, and resulting demands.
• Figure 2: An example of a market whose cooperative market game is not convex.
• Figure 3: Example with two pure traders, a seller $s$ and a buyer $b$. The valuations for the empty bundle are zero for each agent, valuations for bundles not listed in the table are $-\infty$.
• Figure 4: The leximin core imputation cannot be implemented as a competitive equilibrium.
• Figure 5: Market with four essential agents. Each agent $i$'s valuation is given for $\Omega_i = \{ \omega_j, \omega_k \}$ with $j \leq k$.

Theorems & Definitions (68)

• Definition 1
• Definition 2
• Definition 3: Competitive Equilibrium
• Definition 4: Core of Market Outcomes
• Definition 5: milgrom2009substitute
• Example 1: label=counterexample
• Definition 6
• Proposition 1
• Definition 7
• Proposition 2