Stability of equilibrium production-price in a dynamic duopoly Cournot-Bertrand game with asymmetric information and cluster spillovers

Jianjun Long; Hui Huang; Jianjun Long; Hui Huang

doi:10.3934/mbe.2022654

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 14056-14073. doi: 10.3934/mbe.2022654

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Stability of equilibrium production-price in a dynamic duopoly Cournot-Bertrand game with asymmetric information and cluster spillovers

Jianjun Long ¹,
Hui Huang ^{2
,
,}

1.
School of Management Science and Engineering, Chongqing Technology and Business University, Chongqing 400067, China
2.
School of Business, Hunan Agricultural University, Changsha 410128, China

Academic Editor: Xiaodi Li

Received: 12 June 2022 Revised: 13 September 2022 Accepted: 15 September 2022 Published: 22 September 2022

Bounded rationality, asymmetric information and spillover effects are widespread in the economic market, and had been studied extensively in oligopoly games, however, few literature discussed the incomplete information between bounded rational oligopolists in an enterprise cluster. Considering the positive externalities brought by the spillover effect between cluster enterprises, a duopoly Cournot-Bertrand game with bounded rationality and asymmetric information is proposed in this paper. In our model, firm 1 with an information advantage knows all the price information of firm 2 with an information advantage, while firm 2 only partially knows the output information of firm 1, and they adopt boundedly rational expectation and naïve expectation respectively. Interestingly, our theoretical analysis reveals that: (1) When the output adjustment speed of enterprises with information advantage is large or the substitutability between monopoly products is high, moderate effective information is beneficial to the stability of product market, while too low or too high effective information may lead to market disorder. (2) The relationship between cluster spillover and Nash equilibrium stability depends on product substitutability. When the substitutability is small, smaller cluster spillovers are more conducive to the stability of product output or price; when the substitutability is large, the larger the cluster spillover is, the more stable the product market is. Our research has an important theoretical and practical significance to the production-price competition in oligopoly markets.
- Cournot-Bertrand game,
- asymmetric information,
- cluster spillovers,
- bifurcation,
- chaos control
Citation: Jianjun Long, Hui Huang. Stability of equilibrium production-price in a dynamic duopoly Cournot-Bertrand game with asymmetric information and cluster spillovers[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 14056-14073. doi: 10.3934/mbe.2022654

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Abstract

Bounded rationality, asymmetric information and spillover effects are widespread in the economic market, and had been studied extensively in oligopoly games, however, few literature discussed the incomplete information between bounded rational oligopolists in an enterprise cluster. Considering the positive externalities brought by the spillover effect between cluster enterprises, a duopoly Cournot-Bertrand game with bounded rationality and asymmetric information is proposed in this paper. In our model, firm 1 with an information advantage knows all the price information of firm 2 with an information advantage, while firm 2 only partially knows the output information of firm 1, and they adopt boundedly rational expectation and naïve expectation respectively. Interestingly, our theoretical analysis reveals that: (1) When the output adjustment speed of enterprises with information advantage is large or the substitutability between monopoly products is high, moderate effective information is beneficial to the stability of product market, while too low or too high effective information may lead to market disorder. (2) The relationship between cluster spillover and Nash equilibrium stability depends on product substitutability. When the substitutability is small, smaller cluster spillovers are more conducive to the stability of product output or price; when the substitutability is large, the larger the cluster spillover is, the more stable the product market is. Our research has an important theoretical and practical significance to the production-price competition in oligopoly markets.

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