Abstract: A frequent occurrence of emergencies not only poses a threat to society, people's lives as well as property, but also causes great disturbance to supply chain management. One of the serious consequences is the demand disruption. If effective countermeasures are not taken in time, it is likely to lead to profit loss or even breakdown of the supply chain. Especially in the market with multiple competing retailers and under demand uncertainty, since the order quantity of each retailer is not only related to its own retail price, but also affected by his competitors, it is necessary to obtain retailers' equilibrium pricing from their discretionary pricing choices, which makes disruption management more complicated. So this paper will investigate the equilibrium strategies in the supply chain with multiple competing retailers under the demand uncertainty and endogenous price, when the supply chain suffers demand disruption.
Firstly, according to the Kuhn-Tucker theorem, the order quantity of each retailer is analyzed after the demand disruption. Then, according to the supermodel game, a disruption management model of the multi-retailer is constructed, and its equilibrium strategies are analyzed. In the analysis process, a supply chain profit function is expressed as the product of the expected profit generated by the deterministic demand and the comprehensive profit loss coefficient. Based on this coefficient, the comprehensive effect of the profit reduction caused by the demand uncertainty and the extra costs by the demand disruption is investigated. By analyzing the disruption model, the main conclusions can be drawn as follows: after the demand disruption, the pricing game between retailers is a supermodel game, and there is at least one Nash equilibrium solution. If there are multiple Nash equilibriums, they can be ordered, and the optimal equilibrium can reach the optimal expected profit. On this basis, the conditions for the existence of the unique optimal Nash equilibrium solution are analyzed, under which a complete set of equilibrium strategies is obtained, which includes internal equilibrium strategies and corner ones. When all retailers obtain the corner equilibrium strategies, such equilibrium behaviors can be reached only by changing the retails' prices. This shows that it is robust to arrange production plan in advance according to demand forecast and sell products when the selling season comes. Otherwise, retailers need to jointly change the order quantities and retail prices to achieve the equilibrium strategy to deal with demand disruption. Moreover, the price discount sharing mechanism is designed to realize the coordination of decentralized supply chain. Finally, a numerical example is used to demonstrate the effectiveness of the countermeasures, and the results show that when retailers interact with each other effevtively, not only can the price be maintained, but also can greater system profits be obtained. Therefore, it is suggested that a communication platform should be established to facilitate information exchange, jointly prevent and control disruptions, and even coordinate disrupted supply chain, so that the price order can be maintained and recovered as soon as possible, and the disruption management effect can be improved effectively.
The innovation of this paper mainly lies in: (1)Expanding the research on disruption management to the scenario of supply chain with multiple competing retailers under the demand uncertainty and endogenous price, investigating the complete set of the retailers' equilibrium behaviors, and providing quantitative support and decision-making reference for the disruption management from the perspective of analytical solution. (2)Most existing studies adopt a revenue-sharing contract for coordination. However, in a multi-retailer supply chain, the complexity of suppliers' monitoring of retailers' sales revenue increases, and revenue sharing may not be able to be effectively implemented. Therefore, this paper designs a price discount sharing mechanism to coordinate the supply chain. This mechanism has the effect of risk sharing, and when the retailer reduces the price to regulate the market demand, the supplier will provide the retailer with a compensation based on a percentage of the price reduction. So this price mechanism gives the retailer some degree of flexibility, which makes it easy to achieve a long-term cooperation.
In this study, we have not considered the behavioral preferences of retailers, the influence of market power of large retailers or the situation of repeated games in multicycle, which can be expanded in the future.

Key words: demand disruption, supermodular game, equilibrium strategy, price discount sharing scheme

摘要： 在需求突变情景下,针对多零售商竞争型供应链面临不确定性需求且价格内生时的Nash均衡应对策略进行研究。根据库恩—塔克定理,分析各零售商订货量的变化规律,并基于超模博弈,构建多零售商价格竞争的应急模型,分析其均衡应对策略。研究结果表明:需求突变后,零售商之间的价格竞争博弈至少存在一个Nash均衡应对策略,若存在多个Nash均衡策略,则这些策略之间具有优劣次序,最优的均衡应对策略能实现需求突变后各零售商的最大期望利润。并进一步获得了唯一最优Nash均衡策略存在的条件,在该条件下,分析了供应链应对需求突变的完备均衡策略集,从解析解的角度给出该类型供应链的应急策略,为其应急管理提供量化支持与决策参考。此外,设计了价格折扣分担机制来实现分权供应链的协调应对。最后,通过数值算例展示了该均衡应对策略的有效性。

关键词: 需求突变, 超模博弈, 均衡应对策略, 价格折扣分担机制