On the Oscillations in Cournot Games with Best Response Strategies

Zhengyang Liu; Haolin Lu; Liang Shan; Zihe Wang

doi:10.1007/978-981-95-0215-8_24

On the Oscillations in Cournot Games with Best Response Strategies

Zhengyang Liu
, Haolin Lu
, Liang Shan^*
, Zihe Wang

^*Corresponding author for this work

School of Computer Science and Technology

Beijing Institute of Technology
Renmin University of China

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, we consider the dynamic oscillation in the Cournot oligopoly model, which involves multiple firms producing homogeneous products. To explore the oscillation under the updates of best response strategies, we focus on the linear price functions. In this setting, we establish the existence of oscillations. In particular, we show that for the scenario of different costs among firms, the best response converges to either a unique equilibrium or a two-period oscillation. We further characterize the oscillations and propose linear-time algorithms for finding all types of two-period oscillations. To the best of our knowledge, our work is the first step toward fully analyzing the periodic oscillation in the Cournot oligopoly model.

Original language	English
Title of host publication	Computing and Combinatorics - 31st International Computing and Combinatorics Conference, COCOON 2025, Proceedings
Editors	Fedor V. Fomin, Mingyu Xiao
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	320-332
Number of pages	13
ISBN (Print)	9789819502141
DOIs	https://doi.org/10.1007/978-981-95-0215-8_24
Publication status	Published - 2026
Event	31st International Computing and Combinatorics Conference, COCOON 2025 - Chengdu, China Duration: 15 Aug 2025 → 17 Aug 2025

Publication series

Name	Lecture Notes in Computer Science
Volume	15983 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	31st International Computing and Combinatorics Conference, COCOON 2025
Country/Territory	China
City	Chengdu
Period	15/08/25 → 17/08/25

Keywords

Best Response
Cournot Oligopoly Model
Oscillation

Access to Document

10.1007/978-981-95-0215-8_24

Cite this

Liu, Z., Lu, H., Shan, L., & Wang, Z. (2026). On the Oscillations in Cournot Games with Best Response Strategies. In F. V. Fomin, & M. Xiao (Eds.), Computing and Combinatorics - 31st International Computing and Combinatorics Conference, COCOON 2025, Proceedings (pp. 320-332). (Lecture Notes in Computer Science; Vol. 15983 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-981-95-0215-8_24

Liu, Zhengyang ; Lu, Haolin ; Shan, Liang et al. / On the Oscillations in Cournot Games with Best Response Strategies. Computing and Combinatorics - 31st International Computing and Combinatorics Conference, COCOON 2025, Proceedings. editor / Fedor V. Fomin ; Mingyu Xiao. Springer Science and Business Media Deutschland GmbH, 2026. pp. 320-332 (Lecture Notes in Computer Science).

@inproceedings{76aac5e31e3b4e5ab2062e283bc9cfb9,

title = "On the Oscillations in Cournot Games with Best Response Strategies",

abstract = "In this paper, we consider the dynamic oscillation in the Cournot oligopoly model, which involves multiple firms producing homogeneous products. To explore the oscillation under the updates of best response strategies, we focus on the linear price functions. In this setting, we establish the existence of oscillations. In particular, we show that for the scenario of different costs among firms, the best response converges to either a unique equilibrium or a two-period oscillation. We further characterize the oscillations and propose linear-time algorithms for finding all types of two-period oscillations. To the best of our knowledge, our work is the first step toward fully analyzing the periodic oscillation in the Cournot oligopoly model.",

keywords = "Best Response, Cournot Oligopoly Model, Oscillation",

author = "Zhengyang Liu and Haolin Lu and Liang Shan and Zihe Wang",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2026.; 31st International Computing and Combinatorics Conference, COCOON 2025 ; Conference date: 15-08-2025 Through 17-08-2025",

year = "2026",

doi = "10.1007/978-981-95-0215-8\_24",

language = "English",

isbn = "9789819502141",

series = "Lecture Notes in Computer Science",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "320--332",

editor = "Fomin, \{Fedor V.\} and Mingyu Xiao",

booktitle = "Computing and Combinatorics - 31st International Computing and Combinatorics Conference, COCOON 2025, Proceedings",

address = "Germany",

}

Liu, Z, Lu, H, Shan, L & Wang, Z 2026, On the Oscillations in Cournot Games with Best Response Strategies. in FV Fomin & M Xiao (eds), Computing and Combinatorics - 31st International Computing and Combinatorics Conference, COCOON 2025, Proceedings. Lecture Notes in Computer Science, vol. 15983 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 320-332, 31st International Computing and Combinatorics Conference, COCOON 2025, Chengdu, China, 15/08/25. https://doi.org/10.1007/978-981-95-0215-8_24

On the Oscillations in Cournot Games with Best Response Strategies. / Liu, Zhengyang; Lu, Haolin; Shan, Liang et al.
Computing and Combinatorics - 31st International Computing and Combinatorics Conference, COCOON 2025, Proceedings. ed. / Fedor V. Fomin; Mingyu Xiao. Springer Science and Business Media Deutschland GmbH, 2026. p. 320-332 (Lecture Notes in Computer Science; Vol. 15983 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On the Oscillations in Cournot Games with Best Response Strategies

AU - Liu, Zhengyang

AU - Lu, Haolin

AU - Shan, Liang

AU - Wang, Zihe

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2026.

PY - 2026

Y1 - 2026

N2 - In this paper, we consider the dynamic oscillation in the Cournot oligopoly model, which involves multiple firms producing homogeneous products. To explore the oscillation under the updates of best response strategies, we focus on the linear price functions. In this setting, we establish the existence of oscillations. In particular, we show that for the scenario of different costs among firms, the best response converges to either a unique equilibrium or a two-period oscillation. We further characterize the oscillations and propose linear-time algorithms for finding all types of two-period oscillations. To the best of our knowledge, our work is the first step toward fully analyzing the periodic oscillation in the Cournot oligopoly model.

AB - In this paper, we consider the dynamic oscillation in the Cournot oligopoly model, which involves multiple firms producing homogeneous products. To explore the oscillation under the updates of best response strategies, we focus on the linear price functions. In this setting, we establish the existence of oscillations. In particular, we show that for the scenario of different costs among firms, the best response converges to either a unique equilibrium or a two-period oscillation. We further characterize the oscillations and propose linear-time algorithms for finding all types of two-period oscillations. To the best of our knowledge, our work is the first step toward fully analyzing the periodic oscillation in the Cournot oligopoly model.

KW - Best Response

KW - Cournot Oligopoly Model

KW - Oscillation

UR - https://www.scopus.com/pages/publications/105013369448

U2 - 10.1007/978-981-95-0215-8_24

DO - 10.1007/978-981-95-0215-8_24

M3 - Conference contribution

AN - SCOPUS:105013369448

SN - 9789819502141

T3 - Lecture Notes in Computer Science

SP - 320

EP - 332

BT - Computing and Combinatorics - 31st International Computing and Combinatorics Conference, COCOON 2025, Proceedings

A2 - Fomin, Fedor V.

A2 - Xiao, Mingyu

PB - Springer Science and Business Media Deutschland GmbH

T2 - 31st International Computing and Combinatorics Conference, COCOON 2025

Y2 - 15 August 2025 through 17 August 2025

ER -

Liu Z, Lu H, Shan L, Wang Z. On the Oscillations in Cournot Games with Best Response Strategies. In Fomin FV, Xiao M, editors, Computing and Combinatorics - 31st International Computing and Combinatorics Conference, COCOON 2025, Proceedings. Springer Science and Business Media Deutschland GmbH. 2026. p. 320-332. (Lecture Notes in Computer Science). doi: 10.1007/978-981-95-0215-8_24