Based on different carbon quota trading mechanisms, the price and emission reduction strategies of oligopoly manufacturers in the low-carbon market and the government carbon quota mechanism are considered. A dynamic game evolution model of the two oligopoly manufacturers with competitive relations is established. The stability of the equilibrium point of the game model, the price adjustment speed of the decision variable, the impact of carbon emission reduction investment, and the government carbon quota on the system are discussed. Through nonlinear dynamics research, it is found that the advantage of the grandfathering method is that it is conducive to maintaining market stability when the government’s carbon quota decision changes; the advantage of the benchmarking method is that when manufacturers formulate price adjustment strategies, the benchmarking method carbon quota mechanism has a stronger stability range for the market, the manufacturer’s profit price adjustment speed is positively correlated, and the government carbon quota decision and emission reduction investment are also positively correlated. Decision makers need to choose appropriate carbon quota mechanisms and manufacturers’ emission reduction strategies according to actual market changes to maintain supply chain stability.