TY - JOUR

T1 - Optimal pricing policy design for selling cost-reducing innovation in Cournot games

AU - Chen, Mengjing

AU - Huang, Haoqiang

AU - Shen, Weiran

AU - Tang, Pingzhong

AU - Wang, Zihe

AU - Zhang, Jie

N1 - This work was partially supported by Science and Technology Innovation 2030 - “New Generation of Artificial Intelligence” Major Project No. (2018AAA0100903); National Natural Science Foundation of China (Grant No. 61806121); Beijing Outstanding Young Scientist Program (No. BJJWZYJH012019100020098); Intelligent Social Governance Platform, Major Innovation & Planning Interdisciplinary Platform for the “Double-First Class” Initiative, Renmin University of China; a Leverhulme Trust Research Project Grant (2021 – 2024).

PY - 2022/1/12

Y1 - 2022/1/12

N2 - In a marketplace where a number of firms produce and sell a homogeneous product, an innovator develops cost-cutting manufacturing technology and decides to sell it to various firms in the form of a license for profit. Given the innovator's license pricing policy, each firm independently decides whether to purchase the innovation license and how many products to produce. To put it simply, the firms are then in a Cournot market in which the product price is a decreasing function of the total amount of the product on the market. Both the innovator and the firms are acting out of self-interest and look to maximize their utilities. We consider the problem of designing optimal pricing policies for the innovator.A pricing policy could be in the form of a one-off upfront fee, a per-unit royalty fee, or a hybrid of both. Building upon the results of Segal [1], we first show that in a properly designed pricing policy, it is a strictly dominant strategy for the firms to accept the pricing policy, and that this constitutes the unique Nash equilibrium of the game. For the hybrid-fee policy, we devise an algorithm that computes the optimal price in time , where n is the number of firms. For the royalty-fee policy, we show that the problem is captured by convex quadratic programming and can be solved in time , where L is the number of input bits. For the upfront-fee policy, we show the optimal policy problem is NP-complete and we devise an FPTAS algorithm. Moreover, we compare the revenue achievable through the above three pricing policies when all firms are identical.

AB - In a marketplace where a number of firms produce and sell a homogeneous product, an innovator develops cost-cutting manufacturing technology and decides to sell it to various firms in the form of a license for profit. Given the innovator's license pricing policy, each firm independently decides whether to purchase the innovation license and how many products to produce. To put it simply, the firms are then in a Cournot market in which the product price is a decreasing function of the total amount of the product on the market. Both the innovator and the firms are acting out of self-interest and look to maximize their utilities. We consider the problem of designing optimal pricing policies for the innovator.A pricing policy could be in the form of a one-off upfront fee, a per-unit royalty fee, or a hybrid of both. Building upon the results of Segal [1], we first show that in a properly designed pricing policy, it is a strictly dominant strategy for the firms to accept the pricing policy, and that this constitutes the unique Nash equilibrium of the game. For the hybrid-fee policy, we devise an algorithm that computes the optimal price in time , where n is the number of firms. For the royalty-fee policy, we show that the problem is captured by convex quadratic programming and can be solved in time , where L is the number of input bits. For the upfront-fee policy, we show the optimal policy problem is NP-complete and we devise an FPTAS algorithm. Moreover, we compare the revenue achievable through the above three pricing policies when all firms are identical.

KW - Cournot markets

KW - Dominant strategy

KW - Nash equilibrium

KW - Optimal pricing policy

KW - Patent licensing

U2 - 10.1016/j.tcs.2021.12.001

DO - 10.1016/j.tcs.2021.12.001

M3 - Article

SN - 0304-3975

VL - 901

SP - 62

EP - 86

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -