Table 2 Tripartite evolutionary game payment matrix
Agents of the game | Government | ||
|---|---|---|---|
Older adults | Smart Senior Care Technology Service Provider | Strict regulation (\(x\)) | Relaxed regulation (\(1 - x\)) |
Use(\(z\)) | Trustworthy(\(y\)) | \(\begin{gathered} \begin{array}{*{20}{l}} {{S_{g1}} - {M_{g1}} - {B_c} - {B_e} - {N_c} - {N_e},} \\ {{N_c} + {B_c} + {S_c} + {M_e} - {M_{c1}},} \end{array} \hfill \\ {N_e} + {B_e} + {H_{e1}} - {M_e} \hfill \\ \end{gathered}\) | \(\begin{gathered} \begin{array}{*{20}{l}} { - {M_{g2}} - {B_c} - {B_e},} \\ {{B_c} + {M_e} + {S_c} - {M_{c1}},} \end{array} \hfill \\ {B_e} + {H_{e1}} - {M_e} \hfill \\ \end{gathered}\) |
Breach of trust (\(1 - y\)) | \(\begin{gathered} \begin{array}{*{20}{l}} {{S_{g1}} + {L_{c1}} - {M_{g1}} - {B_c} - {B_e} - {N_e},} \\ {{B_c} + c + {M_e} - {L_{c1}} - {L_{c2}} - {M_{c2}},} \end{array} \hfill \\ {L_{c2}} + {N_e} + {B_e} + {H_{e2}} - {M_e} \hfill \\ \end{gathered}\) | \(\begin{gathered} \begin{array}{*{20}{l}} { - {M_{g2}} - {B_c} - {B_e} - {S_{g2}},} \\ {{B_c} + c + {M_e} - {M_{c2}} - {L_{c2}},} \end{array} \hfill \\ {L_{c2}} + {B_e} + {H_{e2}} - {M_e} \hfill \\ \end{gathered}\) | |
No use(\(1 - z\)) | Trustworthy(\(y\)) | \(\begin{gathered} \begin{array}{*{20}{l}} {{S_{g1}} - {B_c} - {N_c} - {M_{g1}},} \\ {{N_c} + {B_c} - {M_{c1}},} \end{array} \hfill \\ 0 \hfill \\ \end{gathered}\) | \(\begin{gathered} \begin{array}{*{20}{l}} { - {M_{g2}} - {B_c},} \\ {{B_c} - {M_{c1}},} \end{array} \hfill \\ 0 \hfill \\ \end{gathered}\) |
Breach of trust (\(1 - y\)) | \(\begin{gathered} \begin{array}{*{20}{l}} {{S_{g1}} + {L_{c1}} - {M_{g1}} - {B_c},} \\ {{B_c} + c - {L_{c1}} - {M_{c2}},} \end{array} \hfill \\ 0 \hfill \\ \end{gathered}\) | \(\begin{gathered} \begin{array}{*{20}{l}} { - {M_{g2}} - {B_c} - {S_{g2}},} \\ {{B_c} + c - {M_{c2}},} \end{array} \hfill \\ 0 \hfill \\ \end{gathered}\) | |