仁本博弈论: 社会偏好理论综析

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

摘要/Abstract

摘要：

社会偏好理论泛化主流经济学的私人效用最大化设定, 假设决策者还额外考虑其行为对他人境况的影响。基本模型中, 决策目标函数为私人与他人效用的加权平均值。《仁本博弈论》采用此设定, 将儒学中的“仁爱”对应为他人效用在决策者目标函数中所占权重, 在超模博弈框架中证明: 仁爱偏好(仁心) 提升利他行为(德行), 从而增益社会福利(义功)。此《仁本博弈论》可视作是针对孔子仁义之道思想的一种模型化尝试。本文系统地梳理了相关的行为博弈第九届中国运筹学会科学技术奖获奖者专辑献, 并与仁本论进行比较。我们发现, 尽管前人已尝试在一般博弈情境下为社会偏好建模, 但均衡分析和结论多数局限在具体博弈情境中, 包括公共物品博弈、囚徒困境和独裁者博弈等等。因此, 已有文献中虽有大量类似“仁生德义”的结论, 但都是情境依赖的。仁本论在一定程度上统一了散落于各情境中的结论。

关键词: 仁本论, 社会偏好, 超模博弈, 儒家哲学, 利他行为, 社会福利

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

中图分类号:

O225

俞宁, 庄尔覃, 曹志刚. 仁本博弈论: 社会偏好理论综析[J]. 运筹学学报（中英文）, 2025, 29(3): 223-242.

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

图/表 1

表1

个体社会偏好效用函数设定类型及其适用场景"

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

表1

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