This article captures price cap regulation under duopoly with game theory approaches. First, price cap regulation reduces price difference, output difference, and price dispersion under both Cournot and Stackelberg competition. Second, price cap regulation weakens the advantages of both costs and first-mover. Third, price cap regulation reduces firms' profits while promotes consumer surplus. Finally, the relationship between the social welfare and price cap regulation is an inverse U-shape. Therefore, optimal price cap regulation exists.