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

Optimal pricing policy design for selling cost-reducing innovation in Cournot games
Optimal pricing policy design for selling cost-reducing innovation in Cournot games
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.
Cournot markets, Dominant strategy, Nash equilibrium, Optimal pricing policy, Patent licensing
0304-3975
62-86
Chen, Mengjing
19f66f94-bf64-4cf9-85f8-482025e48250
Huang, Haoqiang
195ff8a5-28ec-4210-97d9-3d5ee456fb63
Shen, Weiran
74742daf-5cf2-425a-ab23-bd8baf94fd3a
Tang, Pingzhong
be272032-c9fc-4db6-9e89-b251968ba7b1
Wang, Zihe
e4c314c2-e0e0-48d7-9859-a0dab56c74b1
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a
Chen, Mengjing
19f66f94-bf64-4cf9-85f8-482025e48250
Huang, Haoqiang
195ff8a5-28ec-4210-97d9-3d5ee456fb63
Shen, Weiran
74742daf-5cf2-425a-ab23-bd8baf94fd3a
Tang, Pingzhong
be272032-c9fc-4db6-9e89-b251968ba7b1
Wang, Zihe
e4c314c2-e0e0-48d7-9859-a0dab56c74b1
Zhang, Jie
6bad4e75-40e0-4ea3-866d-58c8018b225a

Chen, Mengjing, Huang, Haoqiang, Shen, Weiran, Tang, Pingzhong, Wang, Zihe and Zhang, Jie (2022) Optimal pricing policy design for selling cost-reducing innovation in Cournot games. Theoretical Computer Science, 90, 62-86. (doi:10.1016/j.tcs.2021.12.001).

Record type: Article

Abstract

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.

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More information

Accepted/In Press date: 7 December 2021
e-pub ahead of print date: 10 December 2021
Published date: 12 January 2022
Additional Information: © 2021 Elsevier B.V. All rights reserved
Keywords: Cournot markets, Dominant strategy, Nash equilibrium, Optimal pricing policy, Patent licensing

Identifiers

Local EPrints ID: 454259
URI: http://eprints.soton.ac.uk/id/eprint/454259
ISSN: 0304-3975
PURE UUID: a4748ccb-2a91-41c7-a7d7-b1a583a4de4d

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Date deposited: 03 Feb 2022 17:54
Last modified: 10 Dec 2022 05:01

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Contributors

Author: Mengjing Chen
Author: Haoqiang Huang
Author: Weiran Shen
Author: Pingzhong Tang
Author: Zihe Wang
Author: Jie Zhang

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