演化博弈视角下海外耕地投资参与主体合作行为策略

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Cooperative behavioral strategies of overseas farmland investment participants from the perspective of evolutionary game

WANG Yameng, TIAN Yingdong, DU Panpan, WEI Feng

表3 均衡点的特征值和演化稳定性^③(③ 由于混合策略均衡点E₁₂与E₁₃特征值形式较为复杂,故以

Γ

与

Λ

符号代替。)

Table 3 Eigenvalues and evolutionary stability of equilibrium points

均衡点	特征值	演化稳定性
$E_{1} (0,0, 0)$	$λ_{1} = R_{C 2} - R_{C 4} - R_{t 1} - R_{t 2}$ $λ_{2} = C_{2} + R + R_{t 2} - rSα$ $λ_{3} = rS (- 1 + α) < 0$	若 $λ_{1} < 0 且 λ_{2} < 0$ 同时成立,为稳定点;否则为鞍点
$E_{2} (1,0, 0)$	$λ_{1} = - R_{C 2} + R_{C 4} + R_{t 1} + R_{t 2}$ $λ_{2} = C_{2} + R - R_{t 1} - rSα$ $λ_{3} = rS (- 1 + α) < 0$	若 $λ_{1} < 0$ 和 $λ_{2} < 0$ 同时成立,为稳定点;否则为鞍点
$E_{3} (0,1, 0)$	$λ_{1} = 0$ $λ_{2} = - C_{2} - R - R_{t 2} + rSα$ $λ_{3} = R_{L} > 0$	因为 $λ_{1} = 0$ ,为中心点
$E_{4} (0,0, 1)$	$λ_{1} = 0$ $λ_{2} = - C_{1} - R - R_{L} - R_{t 2} + rS$ $λ_{3} = - rS (- 1 + α) > 0$	因为 $λ_{1} = 0$ ,为中心点
$E_{5} (1,0, 1)$	$λ_{1} = 0$ $λ_{2} = - C_{1} - R - R_{L} + R_{t 1} + rS$ $λ_{3} = - rS (- 1 + α) > 0$	因为 $λ_{1} = 0$ ,为中心点
$E_{6} (1,1, 0)$	$λ_{1} = 0$ $λ_{2} = - C_{2} - R + R_{t 1} + rSα$ $λ_{3} = R_{L} > 0$	因为 $λ_{1} = 0$ ,为中心点
$E_{7} (0,1, 1)$	$λ_{1} = R_{C 1} - R_{C 3} - R_{t 1} - R_{t 2}$ $λ_{2} = C_{1} + R + R_{L} + R_{t 2} - rS$ $λ_{3} = - R_{L} < 0$	若 $λ_{1} < 0$ 和 $λ_{2} < 0$ 同时成立,为稳定点,否则为不稳定点
$E_{8} (1,1, 1)$	$λ_{1} = - R_{C 1} + R_{C 3} + R_{t 1} + R_{t 2}$ $λ_{2} = C_{1} + R + R_{L} - R_{t 1} - rS$ $λ_{3} = - R_{L} < 0$	若 $λ_{1} < 0$ 和 $λ_{2} < 0$ 同时成立,为稳定点,否则为不稳定点
$E_{9} (\frac{C_{2} + R + R_{t 2} - Srα}{R_{t 1} + R_{t 2}}, 1,0)$	$λ_{1} = 0$ $λ_{2} = 0$ $λ_{3} = R_{L} > 0$	因为 $λ_{1} < 0$ , $λ_{2} < 0$ ,为中心点
$E_{10} (\frac{C_{1} + R + R_{L} + R_{t 2} - Sr}{R_{t 1} + R_{t 2}}, 0,1)$	$λ_{1} = 0$ $λ_{2} = - C_{1} + C_{2} - R_{L} + rS - rSα$ $λ_{3} = - rS (- 1 + α) > 0$	因为 $λ_{1} = 0$ ,为中心点
$E_{11} (1, \frac{Sr (- 1 + α)}{- R_{L} - Sr + Srα}, \frac{C_{2} + R - R_{t 1} + R_{L} - Srα}{C_{1} + C_{2} + 2 R + R_{L} - 2 R_{t 1} - Sr - Srα})$	$λ_{1} = \frac{(C_{1} + R + R_{L} - R_{t 1}) (- R_{C 1} + R_{C 3} + R_{t 1} + R_{t 2}) (- 1 + α)}{R_{L} + rS - rSα} λ_{2} = 0$ $λ_{3} = 0$	因为 $λ_{2} = 0$ , $λ_{3} = 0$ ,为中心点
$E_{12} (0, \frac{Sr (- 1 + α)}{- R_{L} - Sr + Srα}, \frac{C_{2} + R + R_{t 2} - Srα}{C_{1} + C_{2} + 2 R + R_{L} + 2 R_{t 2} - Sr - Srα})$	$λ_{1} = Γ_{1}$ $λ_{2} = - Γ_{2}$ $λ_{3} = Γ_{2}$	若 $λ_{1} < 0$ 、 $λ_{2} < 0$ 和 $λ_{3} = 0$ 同时成立,为稳定点,否则为不稳定点
$E_{13} (x^{}, \frac{Sr (- 1 + α)}{- R_{L} - Sr + Srα}, z^{})$	$λ_{1} = Λ_{0}$ $λ_{2} = Λ_{1}$ $λ_{3} = Λ_{2}$	若 $λ_{1} < 0$ 、 $λ_{2} < 0$ 和 $λ_{3} = 0$ 同时成立,为稳定点,否则为不稳定点