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Table 2 Function expressions of variables

From: Reducing the quality risk of elderly care services in government procurement from market-oriented private providers through ex ante policy design: lessons from the principal-agent theory analysis

Expression and definition

Predicated model assumption

x follows a linear uncertainty distribution

√Assumption (1)

\( y(x)=\left\{\begin{array}{l}1,0<x<1\\ {}0,\begin{array}{c}\end{array} others\end{array}\right. \)

√Assumption (2)

U(λ, q(x)) = λ ln q(x)

√Assumption (3)

w(σ, ε, x) = σe−εx2

√Assumption (4)

C(θ, q(x), x) = θ ⋅ q(x)/(x + 3)

√Assumption (5)