基于需求学习的竞争企业的定价和生产决策研究

Study on pricing and production decision for competitive firms with demand learning

文章考虑相互竞争的多个制造型企业,研究它们的最优定价和生产决策.假设一个企业在某期的需求不仅依赖于当期所有企业的价格,而且还依赖于过去时期所有企业的价格.由于企业难以获得需求的确定信息,文章不再假设需求是确定已知或服从某种已知的随机分布,而是考虑未知需求,然后通过需求学习的方法来对未知的需求进行估计和预测.通过建立每个企业的最优控制模型,得出所有企业的最优控制问题是一个广义微分Nash均衡问题.然后,采用微分变分不等式来表述该广义微分Nash均衡问题,并证明了广义微分Nash均衡的存在.介绍了两种不同的需求学习方法来对未知参数进行学习,然后运用固定点算法来求解微分变分不等式.最后,通过数值分析展示了所有企业形成的均衡,并发现相比于基于最小二乘法的需求学习方法,基于马尔科夫链蒙特卡洛的需求学习方法可以使得企业获得更高的利润.

This paper considers pricing and production decision problem for multiple manufacturing firms in an oligopolistic competitive market. Assume a firm＇s demand at a certain period not only depends on the prices of all firms at that period, but also depends on the prices of all firms from the past periods. Since it is very difficult for firms to acquire the deterministic demand information, this paper assumes all firms face unknown demand. This paper models the optimal pricing and production problem for each firm and shows that all firms＇ optimal control problem yields a generalized differential Nash equilibrium problem, which is represented as a differential variational inequality. The authors prove the generalized-differential-Nash equilibrium exists. Two demand learning methods are applied to forecast the unknown demand, and the fixed point algorithm is used to solve the differential variational inequality problem. A numerical example shows the equilibrium that all firms generate, and demonstrates that compared to the demand learning approach based on the least square method, the demand learning approach based on the Markov Chain Monte Carlo can make firms obtain higher profit.