一种齐当别思想下的量子决策模型：对囚徒困境中的分离效应的解释

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辛潇洋, 李瑛(

), 毕研玲, 晏碧华

陕西师范大学心理学院暨陕西省行为与认知神经科学重点实验室, 西安 710062

收稿日期:2018-05-30出版日期:2019-06-25发布日期:2019-04-25
通讯作者:李瑛E-mail:liying@snnu.edu.cn

Quantum decision-making model based on equate-to-differentiate method: Explanation for the disjunction effect in prisoner’s dilemma

XIN Xiaoyang, LI Ying(

), BI Yanling, YAN Bihua

School of Psychology, Shaanxi Normal University & Key Laboratory of Behavioral and Cognitive Neuroscience of Shaanxi Province, Xi’an 710062, China

Received:2018-05-30Online:2019-06-25Published:2019-04-25
Contact:LI Ying E-mail:liying@snnu.edu.cn

摘要/Abstract

摘要： 量子决策模型是近10年来提出的一种新型决策模型, 用以解释那些违背经典决策模型的现象。虽然当前的量子决策模型能够解释囚徒困境中的分离效应, 但其中却存在一些困难, 即会产生反常的概率关系以及无法精确拟合分离效应量较大的实验结果。本研究在分析当前量子决策模型困难的基础上, 结合齐当别思想对模型进行改进和优化。结果表明, 研究所构建的量子决策模型克服了当前模型中的困难, 并且能够预测囚徒困境博弈中由他人收益差距改变而引起的分离效应变化趋势。本研究还是一次启发式决策模型与计算式决策模型相结合的探索。

图/表 5

表1标准囚徒困境博弈中收益矩阵

策略	你选择背叛	你选择合作
对方背叛	你：π_a 对方：π_a	你：π_b 对方：π_c
对方合作	你：π_c 对方：π_b	你：π_d 对方：π_d

表1标准囚徒困境博弈中收益矩阵

策略	你选择背叛	你选择合作
对方背叛	你：π_a 对方：π_a	你：π_b 对方：π_c
对方合作	你：π_c 对方：π_b	你：π_d 对方：π_d

图1Pothos和Busemeyer (2009)量子决策模型中分离效应量以及p(背叛│对手合作) - p(背叛│对手背叛)与u和γ之间关系的3D着色表面图(a-b)与有效区域的着色等高线图(c) (其中t =π/2 )

图1Pothos和Busemeyer (2009)量子决策模型中分离效应量以及p(背叛│对手合作) - p(背叛│对手背叛)与u和γ之间关系的3D着色表面图(a-b)与有效区域的着色等高线图(c) (其中t =π/2 )

表2不同研究中决策者选择背叛的概率以及不同量子决策模型的拟合结果

研究	已知对手背叛	已知对手合作	对手策略未知	绝对误差
Shafir & Tversky (1992)	0.97 (0.79/0.95)	0.84 (0.77/0.84)	0.63 (0.63/0.65)	0.25/0.04
Li & Taplan (2002)	0.73 (0.73/0.77)	0.67 (0.67/0.66)	0.60 (0.67/0.55)	0.07/0.09
Busemeyer et al. (2006)	0.91 (0.80/0.91)	0.84 (0.78/0.84)	0.66 (0.66/0.63)	0.17/0.02
平均值	0.87 (0.79/0.87)	0.78 (0.78/0.78)	0.63 (0.63/0.60)	0.08/0.03

表2不同研究中决策者选择背叛的概率以及不同量子决策模型的拟合结果

研究	已知对手背叛	已知对手合作	对手策略未知	绝对误差
Shafir & Tversky (1992)	0.97 (0.79/0.95)	0.84 (0.77/0.84)	0.63 (0.63/0.65)	0.25/0.04
Li & Taplan (2002)	0.73 (0.73/0.77)	0.67 (0.67/0.66)	0.60 (0.67/0.55)	0.07/0.09
Busemeyer et al. (2006)	0.91 (0.80/0.91)	0.84 (0.78/0.84)	0.66 (0.66/0.63)	0.17/0.02
平均值	0.87 (0.79/0.87)	0.78 (0.78/0.78)	0.63 (0.63/0.60)	0.08/0.03

图2本研究所提出的量子决策模型中p(背叛│对手合作) - p(背叛│对手背叛)以及分离效应量与a和g之间关系的3D着色表面图(其中模型参数b=a/4, t=3π/8)

图3本研究所提出的量子决策模型中收益增加量Δπ与分离效应量之间的关系(模型其余参数为拟合Shafir和Tversky (1992)研究所得参数)

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