Under the background of supply chain competition with deep integration of retail and logistics, market competition has evolved into competition between supply chains. In order to explore the coordination strategy and decision-making mechanism of competition between supply chains, we construct the game models under the coordinated, uncoordinated and mixed scenarios, and solves the equilibrium decisions of supply chain members. On this basis, the effects of coordination strategies on the profits of supply chain members under these three game structures are compared and analyzed. Finally, the models are extended to consider the competition of multiple chains, and the influence of market competition intensity on the decisions and profits of supply chain members are studied. It is found that the coordination strategy is always the dominant strategy of both sides of the competition, and the party who first adopts the coordination strategy can gain a higher market share; when the market demand sensitivity coefficient is low, the dominant strategy under the game equilibrium makes the two sides of the competition fall into the ``prisoner's dilemma", the profits of the supply chain members are mutually damaged and the market customers benefit. Only when the market demand sensitivity coefficient is high, the coordination strategy can make both sides of the competition obtain the compensation of demand expansion, and then a ``win-win" can be achieved. After increasing the number of competitive supply chains, the increasing intensity of competition is conducive to coordinating the two sides to get rid of the ``prisoner's dilemma". The results of numerical analysis verify the feasibility of the proposed models and the theoretical analysis.