Table 1.

Notations and interpretations.

Notations	Interpretations
x	Probability of the doctors choosing fraud strategy
y	Probability of the patients choosing fraud strategy
K 0	Doctors' payoff when they choose non-fraud strategy
K 1	Doctors' payoff when they choose fraud strategy (K0<K1)
N 0	Patients' payoff when they choose non-fraud strategy (N0<N1)
N 1	Patients' payoff when they choose fraud strategy
C 1	Doctors' fraud cost
C 2	Patients' fraud cost
f	Moral hazard coefficient of doctors (0 < f < 1)
g	Moral hazard coefficient of patients (0 < g < 1)
P 1	Punishment of the insurance instructions toward the doctors when they choose fraud strategy
P 2	Punishment of the insurance instructions toward the patients when they choose fraud strategy
R 1	Reward of the insurance instructions toward the doctors when they choose non-fraud strategy
R 2	Reward of the insurance instructions toward the patients when they choose non-fraud strategy
β1	Risk coefficient of doctors when they choose fraud strategy (0 < β1 < 1)
β2	Risk coefficient of patients when they choose fraud strategy (0 < β2 < 1)
H	Bribery given by patients to doctors
M	Extra benefit from insurance instructions when doctors and patients form a collusion
α	Benefit coefficient for doctors when doctors and patients form a collusion (0 < α < 1)