Strategic interaction between institutional investors and supervision department: a theoretical analysis of low-price collusion in SBIC

Li, Xin; Chen, Zhuming

doi:10.1186/s40854-022-00413-x

Financial Innovation

Table 3 local equilibrium points and their corresponding eigenvalue

From: Strategic interaction between institutional investors and supervision department: a theoretical analysis of low-price collusion in SBIC

	\(\lambda_{1}\)	\(\lambda_{2}\)	\(\lambda_{3}\)
\((0,0,0)\)	\(\frac{{\alpha n(p_{L} - p_{1} )(p_{2} - p_{1} )}}{{p_{2} }}( + )\)	\(\frac{{\alpha \eta n(p_{L} - p_{1} )[p_{3} - (1 - k)p_{1} ]}}{{p_{3} }}( + )\)	\(I_{1} - C - I_{2}\)
\((0,0,1)\)	\(\frac{{\alpha n(p_{L} - p_{1} )(p_{2} - p_{1} )}}{{p_{2} }} - M_{1}\)	\(\frac{{\alpha \eta n(p_{L} - p_{1} )[p_{3} - (1 - k)p_{1} ]}}{{p_{3} }} - M_{2}\)	\(- (I_{1} - C - I_{2} )\)
\((0,1,0)\)	\(\frac{{\alpha n(p_{L} - p_{1} )(p_{2} - p_{1} )}}{{p_{2} }}( + )\)	\(- \frac{{\alpha \eta n(p_{L} - p_{1} )[p_{3} - (1 - k)p_{1} ]}}{{p_{3} }}\)	\(I_{1} - C - I_{2} + \frac{1}{2}\lambda N\)
\((1,0,0)\)	\(- \frac{{\alpha n(p_{L} - p_{1} + m)(p_{2} - p_{1} )}}{{p_{2} }}\)	\(\frac{{\alpha \eta n(p_{L} - p_{1} + m)[p_{3} - (1 - k)p_{1} ]}}{{p_{3} }}( + )\)	\(I_{1} - C - I_{2} + \frac{1}{2}\lambda N\)
\((1,1,0)\)	\(- \frac{{\alpha n(p_{L} - p_{1} + m)(p_{2} - p_{1} )}}{{p_{2} }}\)	\(- \frac{{\alpha \eta n(p_{L} - p_{1} + m)[p_{3} - (1 - k)p_{1} ]}}{{p_{3} }}\)	\(I_{1} - C - I_{2} + \lambda N\)
\((1,0,1)\)	\(M_{1} - \frac{{\alpha n(p_{L} - p_{1} + m)(p_{2} - p_{1} )}}{{p_{2} }}( + )\)	\(\frac{{\alpha \eta n(p_{L} - p_{1} + m)[p_{3} - (1 - k)p_{1} ]}}{{p_{3} }} - M_{2}\)	\(- (I_{1} - C - I_{2} + \frac{1}{2}\lambda N)\)
\((0,1,1)\)	\(\frac{{\alpha n(p_{L} - p_{1} )(p_{2} - p_{1} )}}{{p_{2} }} - M_{1}\)	\(M_{2} - \frac{{\alpha \eta n(p_{L} - p_{1} )[p_{3} - (1 - k)p_{1} ]}}{{p_{3} }}( + )\)	\(- (I_{1} - C - I_{2} + \frac{1}{2}\lambda N)\)
\((1,1,1)\)	\(M_{1} - \frac{{\alpha n(p_{L} - p_{1} + m)(p_{2} - p_{1} )}}{{p_{2} }}( + )\)	\(M_{2} - \frac{{\alpha \eta n(p_{L} - p_{1} + m)[p_{3} - (1 - k)p_{1} ]}}{{p_{3} }}( + )\)	\(- (I_{1} - C - I_{2} + \lambda N)\)

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