For achieving the goals of carbon peaking and carbon neutrality, the government will further strengthen subsidies to enterprises for carbon emission reduction. This paper investigates the long-term repeated game behavior of manufacturer and retailer in multichannel supply chains under three different forms of government subsidies. The long-term repeated game behavior of manufacturer and retailer is studied under the manufacturer green innovation subsidy model (IS model), manufacturer production subsidy model (MS model) and retailer sales subsidy model (RS model). Under three situations, excessive price adjustment can easily lead to system instability and sharp fluctuations in profits. Two methods are used for chaos control and management, and the parameter adjustment control method is found having more advantages for system re-stabilization.