Mechanism Design for Efficient Nash Equilibrium in Oligopolistic Markets

TL;DR

This paper proposes a mechanism involving subsidization and taxation to align Nash equilibrium outcomes with the social optimum in oligopolistic markets, ensuring efficient supply dispatch and truthful pricing.

Contribution

It introduces a novel mechanism that guarantees equilibrium efficiency and market self-sufficiency in supply-demand balancing markets with strategic bidding.

Findings

Nash equilibrium exists under mild conditions.

The mechanism achieves efficient supply dispatch and truthful market prices.

Numerical studies validate the mechanism's effectiveness and impact on market outcomes.

Abstract

This paper investigates the efficiency loss in social cost caused by strategic bidding behavior of individual participants in a supply-demand balancing market, and proposes a mechanism to fully recover equilibrium social optimum via subsidization and taxation. We characterize the competition among supply-side firms to meet given inelastic demand, with linear supply function bidding and the proposed efficiency recovery mechanism. We show that the Nash equilibrium of such a game exists under mild conditions, and more importantly, it achieves the underlying efficient supply dispatch and the market clearing price that reflects the truthful system marginal production cost. Further, the mechanism can be tuned to guarantee self-sufficiency, i.e., taxes collected counterbalance subsidies needed. Extensive numerical case studies are run to validate the equilibrium analysis, and we employ individual net profit and a modified version of Lerner index as two metrics to evaluate the impact of the mechanism on market outcomes by varying its tuning parameter and firm heterogeneity.