Table 4 Eigenvalues at different equilibrium points.
From: Dynamic mechanism and evolutionary game analysis of sports industry service transformation
Strategy | Eigenvalue1 | Eigenvalue2 | Eigenvalue3 | Symbol |
|---|---|---|---|---|
\({\pi }_{1}\left(\text{1,1},1\right)\) | \({C}_{m}-M+S\) | \({C}_{u}-H-{\gamma Q}_{u}\) | \({C}_{e}-H-P-S-{\gamma Q}_{e}\) | *** |
\({\pi }_{2}(\text{1,1},0)\) | \(M-{C}_{m}-S\) | \(-H-\zeta \left({C}_{m}-{Q}_{m}+S\right)-\delta \gamma {Q}_{e}\) | \(\zeta {C}_{u}-H-\delta \gamma {Q}_{u}\) | *** |
\({\pi }_{3}(\text{1,0},1)\) | \({C}_{m}-M+S\) | \(H-{C}_{u}+{\gamma Q}_{u}\) | \({Q}_{m}-P-{Q}_{e}-{C}_{m}-2S\) | * + - |
\({\pi }_{4}(\text{1,0},0)\) | \({-\delta Q}_{e}-\zeta ({C}_{m}-{Q}_{m}+S)\) | \({M-C}_{m}-S\) | \(H-\zeta {C}_{u}+\delta \gamma {Q}_{u}\) | ** +  |
\({\pi }_{5}(\text{0,1},1)\) | 0 | \({-C}_{m}-M-P-S\) | \({H-C}_{e}+P+S+\gamma {Q}_{e}\) | *-* |
\({\pi }_{6}(\text{0,1},0)\) | 0 | \({H+\zeta (C}_{m}-{Q}_{m}+S)+\delta \gamma {Q}_{e}\) | \({C}_{m}+M+P+S\) | * +  +  |
\({\pi }_{7}(\text{0,0},1)\) | 0 | \({C}_{m}+P+{Q}_{e}-{Q}_{m}+2S\) | \({-C}_{m}-M-P-{Q}_{m}-S\) | * + - |
\({\pi }_{8}(\text{0,0},0)\) | 0 | \(\delta {Q}_{e}+\zeta ({C}_{m}-{Q}_{m}+S)\) | \({C}_{m}+M+P+{Q}_{m}+S\) | * +  +  |
