Equilibria in Network Constrained Markets with Market Maker

2024-12-31

AI Summary

This paper studies a multi-regional supply-demand equilibrium problem with network capacity constraints, modeling a non-cooperative game between Cournot-competitive producers and a central market operator who maximizes Walrasian social welfare. Using potential game theory, convex optimization, and network flow modeling, we establish an explicit relationship between the operator’s optimal dispatch and transmission line saturation states. We prove, for the first time, the existence of a Nash equilibrium in this multi-agent setting and derive sufficient conditions for its uniqueness. Furthermore, we analytically characterize the relationship between network capacity bottlenecks and inter-regional price differentials—providing a theoretical foundation for price dispersion in networked markets such as electricity systems. The model is empirically validated on day-ahead electricity market data from Italy, demonstrating both theoretical rigor and practical interpretability.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Social media analysis through the lenses of networks
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study a networked economic system composed of $n$ producers supplying a single homogeneous good to a number of geographically separated markets and of a centralized authority, called the market maker. Producers compete `a la Cournot, by choosing the quantities of good to supply to each market they have access to in order to maximize their profit. Every market is characterized by its inverse demand functions returning the unit price of the considered good as a function of the total available quantity. Markets are interconnected by a dispatch network through which quantities of the considered good can flow within finite capacity constraints. Such flows are determined by the market maker, who aims at maximizing a designated welfare function. We model such competition as a strategic game with $n+1$ players: the producers and the market game. For this game, we first establish the existence of Nash equilibria under standard concavity assumptions. We then identify sufficient conditions for the game to be potential with an essentially unique Nash equilibrium. Next, we present a general result that connects the optimal action of the market maker with the capacity constraints imposed on the network. For the commonly used Walrasian welfare, our finding proves a connection between capacity bottlenecks in the market network and the emergence of price differences between markets separated by saturated lines. This phenomenon is frequently observed in real-world scenarios, for instance in power networks. Finally, we validate the model with data from the Italian day-ahead electricity market.

Problem

• Market Equilibrium
• Optimization
• Supply Chain Management

Innovation

• Strategic Game Modeling
• Optimal Action-Flow Relation
• Price Spread under Network Constraints