A Multi-Agent Stackelberg Game for Coordinated Electricity-Price Regulation and Benefit Allocation in Source–Grid–Load–Storage Systems

Abstract

Investment in source-grid-load-storage (SGLS) systems is distorted by market power: renewable, storage and demand-response (DR) agents withhold output and under-build flexibility. This paper formulates a two-level Stackelberg game in which a regulator sets a renewable premium σR (CNY/MWh) and a peak flexibility payment σF (CNY/kW·yr) settled on net peakwindow injection, while three agents play a Nash equilibrium under an endogenous merit-order price and internalize their own price impact. Storage carries SOC dynamics, power limits and a cyclic condition; net-injection settlement removes any reward for charge-discharge churn. The social cost is a resource cost, so premia and tariffs enter as transfers. A Shapley value allocates the cooperative surplus. On a synthetic 80 MW example, the unregulated equilibrium sits 28.9% above the planner's optimum; a price-taking benchmark attributes 26.6 points to market power and 2.3 to unpriced peak/ramping externalities. The instruments (450,400) close 91.7% of the gap, cut annual CO2 from 3.25×105 to 1.13×105 t and the peak from 62.6 to 35.8 MW. One policy applied to four scenarios forfeits 0.22% against clairvoyant per-scenario policies. Under a common budget cap the pair beats the premium alone (83.3%), the flexibility payment alone (11.4%) and all twelve declining-block designs (best 81.0%); a revenue-neutral TOU tariff closes 0.1% and is not used when offered as a third instrument. The Shapley allocation (90.8/5.4/3.8%) lies in the core.