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<p>This paper proposes a dynamic quantum Bertrand duopoly game model with asymmetric information. The stability of equilibrium points for players with adaptive expectations and heterogeneous expectations is studied separately, with a focus on the latter. The impact of various factors on system stability is analyzed, especially quantum entanglement and private information. The research results indicate that if the relationship between quantum entanglement <i>r</i> and product substitution rate <i>b</i> satisfies <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4799_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="102" /> </InlineMediaObject> <EquationSource Format="TEX">\( r&lt;\frac{1}{2}\operatorname {artanh}b\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>&lt;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>artanh</mo> <mi>b</mi> </mrow> </math></EquationSource> </InlineEquation>, the probability parameter <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4799_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> has positive effect on the equilibrium price of Firm 1 with asymmetric information. Moreover, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4799_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> can reduce the stability of the system. If <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4799_Article_IEq4.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="102" /> </InlineMediaObject> <EquationSource Format="TEX">\( r&gt;\frac{1}{2}\operatorname {artanh}b\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>&gt;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>artanh</mo> <mi>b</mi> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4799_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> has negative effect on the equilibrium price of Firm 1 with asymmetric information. In this case, the probability parameter <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4799_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation> contributes to improving the system’s stability. In addition, moderate quantum entanglement enhances system stability, whereas excessive entanglement reduces it.</p>

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Dynamics of quantum Bertrand duopoly games with asymmetric information

  • 期刊论文

  • 发表日期：

    2025年6月13日

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  • Huaxin Chen,
  • Wensheng Jia

摘要

This paper proposes a dynamic quantum Bertrand duopoly game model with asymmetric information. The stability of equilibrium points for players with adaptive expectations and heterogeneous expectations is studied separately, with a focus on the latter. The impact of various factors on system stability is analyzed, especially quantum entanglement and private information. The research results indicate that if the relationship between quantum entanglement r and product substitution rate b satisfies \( r<\frac{1}{2}\operatorname {artanh}b\) r < 1 2 artanh b , the probability parameter \(\theta \) θ has positive effect on the equilibrium price of Firm 1 with asymmetric information. Moreover, \(\theta \) θ can reduce the stability of the system. If \( r>\frac{1}{2}\operatorname {artanh}b\) r > 1 2 artanh b , \(\theta \) θ has negative effect on the equilibrium price of Firm 1 with asymmetric information. In this case, the probability parameter \(\theta \) θ contributes to improving the system’s stability. In addition, moderate quantum entanglement enhances system stability, whereas excessive entanglement reduces it.