Abstract: In order to strengthen strategic cooperation, cross-shareholding among firms in supply chain has become popular. How does cross-shareholding affect operating decisions and performance of supply chain firms? Can cross-shareholding improve the efficiency of supply chain operation and achieve a win-win between the chain's firms and consumers? These have always been hot issues people pay attention to. Although there have been a lot of literature on cross-shareholding between firms in two-tier supply chain, the research on cross-shareholding among firms in three-tier supply chain is very rare. This paper firstly establishes the profit formulation of cross-shareholding among firms by using the mechanism of feedback control. On this basis, conducting Stackelberg pricing game model of firms in three-tier supply chain with cross-shareholding, and carrying out elaborate and tedious mathematical deduction by backward induction, the equilibrium price and profit formula of each firm in the supply chain are derived. The influence of cross-shareholding level on equilibrium market price, firms' profits, consumer surplus and economic welfare is analyzed. The results show that, compared with non-cross-shareholding, only downstream firms' one-way shareholding in upstream firms has no effect on the supply chain performance. Properly increasing upstream firms' shareholding in downstream firms, while restricting downstream firms' shareholding in upstream firms, can effectively lower market price, increase the chain's total profit and all firms' profits, raise consumer surplus, and improve economic welfare, so as to realize a win-win situation between firms in the supply chain and consumers.

Key words: supply chain, cross-shareholding, equilibrium pricing, market performance, Stackelberg game

摘要： 本文构建三级供应链企业间纵向交叉持股时的Stackelberg定价博弈模型,采用逆推归纳法推演出供应链各厂商交叉持股时的均衡定价及其利润公式,分析了交叉持股对三级供应链均衡市场价格、厂商利润、消费者剩余和经济福利的影响。研究结果表明,较之无交叉持股,仅下游厂商对上游厂商单向持股,对供应链的绩效没有影响;而适当增大上游厂商对下游厂商持股,限制下游厂商对上游厂商持股,能有效降低市场价格,提高供应链及各厂商的利润,增加消费者剩余,改善经济福利,实现供应链各厂商与消费者的共赢。

关键词: 供应链, 交叉持股, 均衡定价, 市场绩效, Stackelberg博弈