Table 1 Payoff matrix of the game system involving the local government, superior medical institutions, and patients

S

S

S

\(I - C_{g} - T + D\)

\((W_{1} - S_{1} )(1 - n) + T\)

\(Q_{1} - C_{1}\)

S

S

O

\(I - C_{g} - T - U\)

\((W_{1} - S_{1} )(1 - n) + T\)

\(Q_{3} - C_{3}\)

S

O

S

\(I - C_{g}\)

\((W_{1} - S_{1} )(1 - n)\)

\(Q_{1} - C_{1}\)

S

O

O

\(- C_{g} - M + H\)

\((W_{2} - S_{2} ) - H\)

\(Q_{2} - C_{2}\)

O

S

S

\(I\)

\((W_{1} - S_{1} )(1 - n)\)

\(Q_{1} - C_{1}\)

O

S

O

\(I + L\)

\((W_{1} - S_{1} )(1 - n) - L\)

\(Q_{3} - C_{3}\)

O

O

S

\(I - P\)

\((W_{1} - S_{1} )(1 - n)\)

\(Q_{1} - C_{1}\)

O

O

O

\(- M - P\)

\(W_{2} - S_{2}\)

\(Q_{2} - C_{2}\)