Table 1 Payment matrix.
| Â | Public | ||
|---|---|---|---|
Participate \((\alpha )\) | non-participation \((1 - \alpha )\) | ||
strict supervision\((\gamma )\) | Compliant transportation\((\beta )\) | \(\begin{gathered} {R_s}+W - {C_s} \hfill \\ {R_{t1}} - {C_{t1}} \hfill \\ {R_{p1}} \hfill \\ \end{gathered}\) | \(\begin{gathered} {R_s}+W - {C_s} \hfill \\ {R_{t1}} - {C_{t1}} \hfill \\ {R_{p2}} \hfill \\ \end{gathered}\) |
Non-compliant transportation\((1 - \beta )\) | \(\begin{gathered} W+{R_s}+\theta {V_{t2}} - {C_s} \hfill \\ {R_{t1}}+{R_{t2}} - {C_{t2}} - \theta {V_{t2}} - \mu {B_t} \hfill \\ {R_{p1}} \hfill \\ \end{gathered}\) | \(\begin{gathered} W+{R_s}+\theta {V_{t2}} - {C_s} \hfill \\ {R_{t1}}+{R_{t2}} - {C_{t2}} - \theta {V_{t2}} \hfill \\ {R_{P2}} \hfill \\ \end{gathered}\) | |
Lax regulation\((1 - \gamma )\) | Compliant transportation\((\beta )\) | \(\begin{gathered} {R_S} - {C_s} \hfill \\ {R_{t1}} - {C_{t1}} \hfill \\ {R_{p1}} \hfill \\ \end{gathered}\) | \(\begin{gathered} {R_s} - {C_s} \hfill \\ {R_{t1}} - {C_{t1}} \hfill \\ {R_{p2}} \hfill \\ \end{gathered}\) |
Non-compliant transportation\((1 - \beta )\) | \(\begin{gathered} {R_s}+{R_{bs}} - {C_s} - \mu {B_s} \hfill \\ {R_{t1}}+{R_{t2}} - {C_{t2}} - {C_c} - \mu {B_t} \hfill \\ {R_{p1}} - (1 - \mu ){C_p} \hfill \\ \end{gathered}\) | \(\begin{gathered} {R_s}+{R_{bs}} - {C_s} \hfill \\ {R_{t1}}+{R_{t2}} - {C_{t2}} - {C_c} \hfill \\ {R_{p2}} - {C_p} \hfill \\ \end{gathered}\) | |
