Table 2 The payoff matrix for participants.

From: Understanding social insurance contribution evasion through evolutionary game theory: insights from China

Strategy Choice

Local Government

 
 

Strict collection (\(x\))

Lax collection (\(1-x\))

Enterprise

Compliance (\(y\))

Employee

Active engagement (\(z\))

\(\left[\begin{array}{l}(1+\varphi )S-{C}_{GS}+{B}_{G}\\ (1+\alpha ){R}_{FC}-S\\ {R}_{E}-\varphi S-{C}_{ER}\end{array}\right]\)

\(\left[\begin{array}{l}(1+\varphi )S-{C}_{GL}\\ (1+\alpha ){R}_{FC}-S\\ {R}_{E}-\varphi S-{C}_{ER}\end{array}\right]\)

Passive response (\(1-z\))

\(\left[\begin{array}{l}(1+\varphi )S-{C}_{GS}+{B}_{G}\\ {R}_{FC}-S\\ {R}_{E}-\varphi S-{P}_{E}\end{array}\right]\)

\(\left[\begin{array}{l}(1+\varphi )S-{C}_{GL}\\ {R}_{FC}-S\\ {R}_{E}-\varphi S-{P}_{E}\end{array}\right]\)

Evasion (\(1-y\))

Employee

Active engagement (\(z\))

\(\left[\begin{array}{l}(1+\varphi )\eta S-{C}_{GS}+{P}_{F}-{B}_{E}+{B}_{G}\\ {R}_{FE}-\eta S-{P}_{F}\\ \theta {R}_{E}+{B}_{E}-\varphi \eta S-{C}_{EJ}\end{array}\right]\)

\(\left[\begin{array}{l}(1+\varphi )\eta S-{C}_{GL}+{P}_{F}-{B}_{E}-{P}_{G}\\ {R}_{FE}-\eta S-{P}_{F}\\ \theta {R}_{E}+{B}_{E}-\varphi \eta S-{C}_{EJ}\end{array}\right]\)

Passive response (\(1-z\))

\(\left[\begin{array}{l}(1+\varphi )\eta S-{C}_{GS}+{P}_{F}+{B}_{G}\\ {R}_{FE}-\eta S-{P}_{F}\\ \theta {R}_{E}-\varphi \eta S\end{array}\right]\)

\(\left[\begin{array}{l}(1+\varphi )\eta S-{C}_{GL}-{P}_{G}\\ {R}_{FE}-\eta S\\ \theta {R}_{E}-\varphi \eta S\end{array}\right]\)