Table 3 Payoff matrix of three governments.
From: Fiscal centralization versus decentralization of transport infrastructure operation and maintenance
Strategies | Expected payoffs | ||
|---|---|---|---|
Central government | Local government A | Local government B | |
(x, y, z) | \({R}_{A}{+R}_{B}-{C}_{1}-{C}_{3}\) \(-\left({T}_{{rA}}+{T}_{{rB}}\right)\) | \(\sigma {R}_{A}{+\omega \left(1-\tau \right)R}_{B}{+T}_{{rA}}\) \(-{E}_{A}^{2}/2-{C}_{3A}\) | \(\tau {R}_{B}{+\varphi \left(1-\sigma \right)R}_{A}{+T}_{{rB}}\) \(-{E}_{B}^{2}/2-{C}_{3B}\) |
(x, y, 1-z) | \({R}_{A}{+\nu R}_{B}-{C}_{1}-{C}_{3}\) \(-{T}_{{rA}}+{F}_{B}\) | \(\sigma {R}_{A}{+\omega \left(1-\tau \right)\nu R}_{B}{+T}_{{rA}}\) \(-{E}_{A}^{2}/2-{C}_{3A}+b{Q}_{B}\) | \(\tau {\nu R}_{B}{+\varphi \left(1-\sigma \right)R}_{A}\) \(-{\mu }_{B}{E}_{B}^{2}/2-{Q}_{B}-{F}_{B}\) |
(x, 1-y, z) | \({\varepsilon R}_{A}{+R}_{B}-{C}_{1}-{C}_{3}\) \(-{T}_{{rB}}+{F}_{A}\) | \(\sigma {\varepsilon R}_{A}{+\omega \left(1-\tau \right)R}_{B}\) \(-{\mu }_{A}{E}_{A}^{2}/2-{Q}_{A}-{F}_{A}\) | \(\tau {R}_{B}{+\varphi \left(1-\sigma \right)\varepsilon R}_{A}{+T}_{{rB}}\) \(-{E}_{B}^{2}/2-{C}_{3B}+a{Q}_{A}\) |
(x, 1-y, 1-z) | \({\varepsilon R}_{A}{+\nu R}_{B}-{C}_{1}-{C}_{3}\) \(+\left({F}_{A}+{F}_{B}\right)\) | \(\sigma {\varepsilon R}_{A}{+\omega \left(1-\tau \right)\nu R}_{B}\) \(-{\mu }_{A}{E}_{A}^{2}/2-{F}_{A}\) | \(\tau \vartheta {R}_{B}{+\varphi \left(1-\sigma \right)\varepsilon R}_{A}\) \(-{\mu }_{B}{E}_{B}^{2}/2-{F}_{B}\) |
(1-x, y, z) | \({R}_{A}{+R}_{B}-{\theta C}_{1}\) \(-\left(\alpha {T}_{{rA}}+{\beta T}_{{rB}}\right)\) | \(\sigma {R}_{A}{+\omega \left(1-\tau \right)R}_{B}{+\alpha T}_{{rA}}\) \(-{E}_{A}^{2}/2-{C}_{3A}\) | \(\tau {R}_{B}{+\varphi \left(1-\sigma \right)R}_{A}{+\beta T}_{{rB}}\) \(-{E}_{B}^{2}/2-{C}_{3B}\) |
(1-x, y, 1-z) | \({R}_{A}{+\nu R}_{B}-{\theta C}_{1}\) \(-{\alpha T}_{{rA}}+\delta {F}_{B}\) | \(\sigma {R}_{A}{+\omega \left(1-\tau \right)\nu R}_{B}{+\alpha T}_{{rA}}\) \(-{E}_{A}^{2}/2-{C}_{3A}+b{Q}_{B}\) | \(\tau {\nu R}_{B}{+\varphi \left(1-\sigma \right)R}_{A}\) \(-{\mu }_{B}{E}_{B}^{2}/2-{Q}_{B}-{\delta F}_{B}\) |
(1-x, 1-y, z) | \({\varepsilon R}_{A}{+R}_{B}-\theta {C}_{1}\) \(-{\beta T}_{{rB}}+{\gamma F}_{A}\) | \(\sigma {\varepsilon R}_{A}{+\omega \left(1-\tau \right)R}_{B}\) \(-{\mu }_{A}{E}_{A}^{2}/2-{Q}_{A}-\gamma {F}_{A}\) | \(\tau {R}_{B}{+\varphi \left(1-\sigma \right)\varepsilon R}_{A}{+\beta T}_{{rB}}\) \(-{E}_{B}^{2}/2-{C}_{3B}+a{Q}_{A}\) |
(1-x, 1-y, 1-z) | \({\varepsilon R}_{A}{+\nu R}_{B}-\theta {C}_{1}\) \(+{\gamma F}_{A}+\delta {F}_{B}\) | \(\sigma {\varepsilon R}_{A}{+\omega \left(1-\tau \right)\nu R}_{B}\) \(-{\mu }_{A}{E}_{A}^{2}/2-\gamma {F}_{A}\) | \(\tau {\nu R}_{B}{+\varphi \left(1-\sigma \right)\varepsilon R}_{A}\) \(-{\mu }_{B}{E}_{B}^{2}/2-{\delta F}_{B}\) |
