Under the construction of a unified national market

coal-fired generation units are required to fully participate in the coal and electricity market. Massive coal-fired generation units can establish an interaction between coal and electricity prices

significantly shaping how the market operates. This paper investigates this issue from the perspective of non-cooperative game. Firstly

the operational model of coal-fired generation units and their decision model for participating in coal and electricity markets are proposed to construct the non-cooperative differential game. Secondly

based on the mean-field theory

the dimensionality of the large-scale game is effectively reduced. Then

the mean-field differential game problem is transformed into a min-max saddle point problem

and the proximal primal-dual gradient descent algorithm is used to generate analytical iterations. Drawing on a Northwest China case study

this paper explores the interaction between coal and electricity prices under two scenarios: the stable coal supply and the coal supply shortage. The study reveals: the coal inventory of coal-fired enterprises can effectively suppress price peaks in the coal and electricity markets; during periods of insufficient power supply caused by coal shortages

profit-driven stockpiling by coal-fired enterprises creates a spillover effect. Finally

this paper proposes operational and regulatory suggestions for the coal and electricity markets based on these phenomena.