Abstract: In the network markets of product families,a complex game problem played by a leader with dual goals (maximizing its profits and total consumer surplus) and multiple followers maximizing their profits was studied.Based on the theories of two-layer programming,NSGA-Ⅱ,and Cournot game,a two-layer programming algorithm with games was designed to solve the problem.The elite strategy was used to improve the algorithm's searching performance and convergence speed,and numerical examples were used to analyze the performance of the algorithm.The networked markets competition problem of product families was solved based on this algorithm and the approximate equilibrium solution set was obtained.The study showed that the smaller (larger) the demand slope of the product variety segment where the leader involved,the better for the leader who focused on its profits (total consumer surplus);the ripple effect existed in the network,and the capacity constraint of each product variety could suppress the ripple effect,but the total capacity constraint of the firms would amplify the ripple effect;the leader firm was more aggressive in market expansion than the follower firms;the leader preferred the alliance method of "attacking the closer firms with the distant firms",but follower preferred the alliance method of "attacking the distant firms with the closer firms" to each other.

Key words: product family, network markets, bi-objective optimization, two-level planning, Cournot game, capacity constraints

摘要： 在具有产能约束的产品族网络市场中,研究一个具有双目标的领导者(自身利润和总消费者剩余最大化),以及多个以各自利润最大化为目标的跟随者,形成的复杂博弈问题。基于双层规划思想、带精英策略的快速非支配排序遗传算法和古诺博弈理论,设计一种含博弈的双层规划算法,采用精英策略提高算法的寻优能力和收敛速度,并运用数值算例分析算法的性能。基于该算法求解产品族网络市场竞争问题,得到网络均衡解集。研究发现:①领导者参与的产品变体细分市场的需求斜率越小(大)对关注自身利润(总消费者剩余)目标的领导者越有利;②网络中存在涟漪效应,产品变体产能约束能够抑制这种涟漪效应,但是企业总产能约束反而会加大涟漪效应;③在网络市场拓展中,领导者比跟随者更具有市场侵略性;④领导者更倾向于选择“远交近攻”的联盟方式,但跟随者之间更倾向于选择“近交远攻”的联盟方式。

关键词: 产品族, 网络市场, 双目标优化, 双层规划, 古诺博弈, 产能约束