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Table 3 Equilibrium point determination status

From: An evolutionary game-based simulation study of a multi-agent governance system for smart senior care services in China

Equalization points

Eigenvalue

\(\lambda\) 1

\(\lambda\) 2

\(\lambda\) 3

1 (0, 0, 0)

\({S_{g1}} + {L_{c1}} - {M_{g1}} + {M_{g2}} + {S_{g2}}\)

\({M_{c2}} - c - {M_{c1}}\)

\({L_{c2}} + {B_e} - {M_e} + {H_{e2}}\)

2 (0, 0, 1)

\({S_{g1}} + {L_{c1}} - {M_{g1}} + {M_{g2}} + {S_{g2}} - {N_e}\)

\({S_c} + {L_{c2}} - {M_{c1}} - c + {M_{c2}}\)

\({M_e} - {L_{c2}} - {B_e} - {H_{e2}}\)

3 (0, 1, 1)

\({S_{g1}} - {N_c} - {M_{g1}} + {M_{g2}} - {N_e}\)

\({M_{c1}} + c - {M_{c2}} - {S_c} - {L_{c2}}\)

\({M_e} - {H_{e1}} - {B_e}\)

4 (0, 1, 0)

\({S_{g1}} - {N_c} - {M_{g1}} + {M_{g2}}\)

\({M_{c1}} + c - {M_{c2}}\)

\({H_{e1}} + {B_e} - {M_e}\)

5 (1, 0, 0)

\({M_{g1}} - {S_{g1}} - {L_{c1}} - {M_{g2}} - {S_{g2}}\)

\({N_c} + {L_{c1}} - {M_{c1}} - c + {M_{c2}}\)

\({N_e} + {L_{c2}} + {B_e} - {M_e} + {H_{e2}}\)

6 (1, 0, 1)

\({M_{g1}} + {N_e} - {S_{g1}} - {L_{c1}} - {M_{g2}} - {S_{g2}}\)

\({S_c} + {L_{c2}} + {N_c} + {L_{c1}} - {M_{c1}} - c + {M_{c2}}\)

\({M_e} - {N_e} - {L_{c2}} - {B_e} - {H_{e2}}\)

7 (1, 1, 0)

\({N_c} + {M_{g1}} - {S_{g1}} - {M_{g2}}\)

\({M_{c1}} + c - {N_c} - {L_{c1}} - {M_{c2}}\)

\({H_{e1}} + {N_e} + {B_e} - {M_e}\)

8 (1, 1, 1)

\({N_c} + {M_{g1}} + {N_e} - {S_{g1}} - {M_{g2}}\)

\({M_{c1}} + c - {S_c} - {L_{c2}} - {N_c} - {L_{c1}} - {M_{c2}}\)

\({M_e} - {H_{e1}} - {N_e} - {B_e}\)