仁本博弈论: 社会偏好理论综析

doi:10.15960/j.cnki.issn.1007-6093.2025.03.011

Abstract

Abstract:

Social preference theory generalizes the standard assumption of self-regarding utility maximization in economics, and allows decision-makers to take into account the effect of own behavior on others. In the basic model, the objective function is a weighted average of one's own utility and that of others. "Confucian Game Theory" adopts this framework, associating an individual's level of empathy-based benevolence with the weight assigned to others' utility in their objective function. Within a supermodular game framework, they prove that benevolence (ren motive) enhances altruistic behavior (de behavior), which in turn improves overall social welfare (yi consequence). This "Confucian Game Theory" provides a behavioral scientific foundation for Confucian philosophy. This paper systematically reviews the related behavioral game theory literature and compares it with "Confucian Game Theory". We find that although earlier models of social preferences are formulated generally, the existing equilibrium analysis usually focuses on specific contexts such as public goods games, the prisoner's dilemma, and dictator games. Consequently, while previous studies have derived many conclusions in the same vein as "ren improves de and yi", those results are often context-dependent. In a sense, Confucian Game Theory unifies conclusions that are scattered across myriad contexts.

Key words: residing in ren, social preferences, supermodular game, confucian philosophy, altruistic behavior, social welfare

CLC Number:

O225

Ning YU, Ertan ZHUANG, Zhigang CAO. Confucian game theory: A synthesis of social preference theory[J]. Operations Research Transactions, 2025, 29(3): 223-242.

Figures/Tables 1

适用场景	文献	社会偏好效用函数	设定类型
公共物品博弈	[36]	$ U_i(x) = \pi_i(x) + \lambda \sum\limits_{j \in I } \pi_j(x) $	Ⅰ
	[17]	$ U_i(x) = u_i(x) + \sum\limits_{j \in I \setminus \{i\}} \frac{a_i+\lambda a_j}{1+\lambda} u_j(x) $	Ⅰ
	[19]	$ U_i(x) = \pi_i(x) - \frac{\alpha_i}{n-1} \sum_{j \neq i} \max \{\pi_j(x) - \pi_i(x), 0\} - \frac{\beta_i}{n-1} \sum_{j \neq i} \max \{\pi_i(x) - \pi_j(x), 0\} $ ^a	Ⅱ
	[12]	$ U_i(x) = [\alpha \pi_i(x)^\rho + (1-\alpha)\pi_j(x)^\rho]^{1/\rho} $	Ⅳ
	[23]	$ U_i(f, x_i'', x_i') = \pi_i(f) + \rho_i \sum\limits_{n \to f, n \in N_i} \varphi_j(n, x_i'', x_i') \sigma_i(n, f, x_i'', x_i') $	Ⅲ
	[40]	$ U_i(x) = \pi_i(x)- s_i(x_i) + \sum\limits_{j \in I\setminus \{i\}} \left[(a_i + \lambda_i b_j)(\pi_j(x) - s_{ij}) - c_i(s_{ij})\right] $ ^b	Ⅱ
	[13]	$ U_i(x) = \pi_i(x)+\alpha_i \pi_j(x) $	Ⅰ
	[38]	$ U_i(x, y) = \pi_i(x)+\alpha \pi_j(x) $	Ⅰ
囚徒困境	[41]	$ U_i(b_i, \sigma) := \sum_{t \in A} P_\sigma(\pi) \bar{u}_i(b_i, \pi) $ ^c	Ⅲ
	[11]	$ U_i(x_i, x'_i, x''_i) = \pi_i(x_i, x'_i) + \tilde{f}_j(x'_i, x''_i) \left[1 + f_i(x_i, x'_i)\right] $ ^d	Ⅲ
	[20]	$ U_i(x) = U_i(\pi_i(x), \frac{\pi_i(x)}{\sum_{j\in I}\pi_j(x)}) $	Ⅳ
	[12]	$ U_i(x) = [\alpha \pi_i(x)^\rho + (1-\alpha)\pi_j(x)^\rho]^{1/\rho} $	Ⅳ
	[22]	$ U_i=\pi_i+\lambda_i \sum_{j\in I\setminus\{ i\}}f_{ij} \tilde{f}_{iji} $ ^e	Ⅲ
	[23]	$ U_i(f, x_i'', x_i') = \pi_i(f) + \rho_i \sum\limits_{n \to f, n \in N_i} \varphi_j(n, x_i'', x_i') \sigma_i(n, f, x_i'', x_i') $	Ⅲ
	[29]	$ U_i(x) = \pi_i(x)+r\pi_j(x) $	Ⅰ
独裁者博弈	[19]	$ U_i(x) = \pi_i(x) - \frac{\alpha_i}{n-1} \sum_{j \neq i} \max \{\pi_j(x) - \pi_i(x), 0\} - \frac{\beta_i}{n-1} \sum_{j \neq i} \max \{\pi_i(x) - \pi_j(x), 0\} $	Ⅱ
	[20]	$ U_i(x) = U_i(\pi_i(x), \frac{\pi_i(x)}{\sum_{j\in I}\pi_j(x)}) $	Ⅳ
	[12]	$ U_i(x) = [\alpha \pi_i(x)^\rho + (1-\alpha)\pi_j(x)^\rho]^{1/\rho} $	Ⅳ
	[39]	$ U_i(x) = (1-\lambda)\pi_i(x) + \lambda_i [\delta_i \min_{j\in I} \pi_j(x)+(1-\delta_i)\sum_{k\in I}\pi_k] $	Ⅱ
	[23]	$ U_i(f, x_i'', x_i') = \pi_i(f) + \rho_i \sum\limits_{n \to f, n \in N_i} \varphi_j(n, x_i'', x_i') \sigma_i(n, f, x_i'', x_i') $	Ⅲ
最后通牒博弈	[17]	$ U_i(x) = u_i(x) + \sum\limits_{j \in I \setminus \{i\}} \frac{a_i+\lambda a_j}{1+\lambda} u_j(x) $	Ⅰ
	[19]	$ U_i(x) = \pi_i(x) - \frac{\alpha_i}{n-1} \sum_{j \neq i} \max \{\pi_j(x) - \pi_i(x), 0\} - \frac{\beta_i}{n-1} \sum_{j \neq i} \max \{\pi_i(x) - \pi_j(x), 0\} $	Ⅱ
	[20]	$ U_i(x) = U_i(\pi_i(x), \frac{\pi_i(x)}{\sum_{j\in I}\pi_j(x)}) $	Ⅳ
	[37]	$ U_i(x) = \pi_i(x) + \alpha_i \pi_j(x) + \varepsilon_i $ ^f	Ⅰ
	[23]	$ U_i(f, x_i'', x_i') = \pi_i(f) + \rho_i \sum\limits_{n \to f, n \in N_i} \varphi_j(n, x_i'', x_i') \sigma_i(n, f, x_i'', x_i') $	Ⅲ
	[56]	$ U_i(x) = \pi_i(x) + \pi_j(x) - \alpha_i \max \{\pi_j(x) - \pi_i(x), 0\} - \beta_i \max \{\pi_i(x) - \pi_j(x), 0\} $	Ⅱ
信任博弈	[11]	$ U_i(x_i, x'_i, x''_i) = \pi_i(x_i, x'_i) + \tilde{f}_j(x'_i, x''_i) \left[1 + f_i(x_i, x'_i)\right] $	Ⅲ
	[17]	$ U_i(x) = u_i(x) + \sum\limits_{j \in I \setminus \{i\}} \frac{a_i+\lambda a_j}{1+\lambda} u_j(x) $	Ⅰ
礼物交换博弈	[20]	$ U_i(x) = U_i(\pi_i(x), \frac{\pi_i(x)}{\sum_{j\in I}\pi_j(x)}) $	Ⅳ
	[23]	$ U_i(f, x_i'', x_i') = \pi_i(f) + \rho_i \sum\limits_{n \to f, n \in N_i} \varphi_j(n, x_i'', x_i') \sigma_i(n, f, x_i'', x_i') $	Ⅲ
拍卖	[17]	$ U_i(x) = u_i(x) + \sum\limits_{j \in I \setminus \{i\}} \frac{a_i+\lambda a_j}{1+\lambda} u_j(x) $	Ⅰ
	[19]	$ U_i(x) = \pi_i(x) - \frac{\alpha_i}{n-1} \sum_{j \neq i} \max \{\pi_j(x) - \pi_i(x), 0\} - \frac{\beta_i}{n-1} \sum_{j \neq i} \max \{\pi_i(x) - \pi_j(x), 0\} $	Ⅱ
	[20]	$ U_i(x) = U_i(\pi_i(x), \frac{\pi_i(x)}{\sum_{j\in I}\pi_j(x)}) $	Ⅳ
投票博弈	[15]	$ U(x, \mathbf{x}_{-i}^{(n-1)}) = \sum_{m=1}^{n} \binom{n-1}{m-1} \kappa^{m-1} (1-\kappa)^{n-m} \pi(x, \mathbf{x}^{(m-1)}, \mathbf{x}_{-i}^{(n-m)}) $ ^g	Ⅳ
网络博弈	[14]	$ U_i(x) = \pi_i(x) + \sum_{j \neq i} \lambda_{ij} \pi_j(x) $	Ⅰ
	[18]	$ U_i(x) = u_i(x)+\min_{j\in I} u_j(x) $	Ⅱ
亲缘博弈	[10]	$ U_i(x) = U_i(\pi_i(x), \pi_{-i}(x)) $	Ⅳ
	[16]	$ U_t = G(U_{t-1}, u_t, U_{t+1}) $ ^h	Ⅳ
	[25]	$ U_i(x) = \pi_i(x)+\alpha_i \pi_{-i}(x) $	Ⅰ
	[38]	$ U_i(x) = \pi_i(x)+\alpha \pi_j(x) $	Ⅰ
	[42]	$ u_i(x_i, \mathbf{x}_{-i}) = (1 - \kappa) \cdot \pi(x_i, \mathbf{x}_{-i}) + \kappa \cdot \pi(x_i, \mathbf{x}_{i}) $ ⁱ	Ⅳ
	[44]	$ U_i(x) = U_i(\pi_i(x), \pi_{-i}(x), \pi^*(x)) $ ^j	Ⅳ
	[29]	$ U_i(x) = \pi_i(x)+r\pi_j(x) $	Ⅰ

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Confucian game theory: A synthesis of social preference theory

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