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

doi:10.3724/SP.J.1041.2019.00724

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。

关键词: 量子, 决策, 齐当别, 分离效应, 囚徒困境

Abstract:

One of the most puzzling findings in decision research field is the disjunction effect. Several studies demonstrate that the disjunction effect exists in a two-person prisoner’s dilemma game. This effect violates the sure-thing principle and cannot be explained by classical decision-making models. During the recent decade, quantum decision making models have been established on the basis of the mathematical structure and methodologies of quantum mechanics. Owing to their special theoretical structures, quantum decision-making models are well suited for explaining the disjunction effect, although these models continue to encounter difficulties.

This study aims to overcome the difficulties in existing quantum decision-making models by developing a modified model. To achieve this goal, the deficiencies of the previous models were analyzed. We concluded three deficiencies: 1) Although previous quantum decision-making models can account for the disjunction effect, they can also obtain findings that defy the experimental results and common sense. 2) They cannot explain the disjunction effect with large values in certain experiments (e.g., the experiment of Shafir & Tversky, 1992). 3) They cannot properly illustrate the relationship between the utility of decision maker’s pay off and the scale of the disjunction effect.

The reasons for these difficulties were investigated. An important reason is that previous quantum decision-making models ignore that the decision maker may consider another’s pay off based on different decision conditions. Another reason is the over-simplicity of the utility function. With the above analyses as basis, we adopted the equate-to-differentiate method to rebuild the quantum decision-making model. In this new model, whether the decision maker considers another’s pay off or not based on a specific decision condition is determined with the equate-to-differentiate method. In addition, the utility function is redefined by value function and hyperbolic tangent transformation.

Results revealed that the new quantum decision-making model overcomes the difficulties in previous quantum decision-making models. The proposed model is an integration of heuristic and computational or mathematical models. This ideal model integration deserves much attention and has good theoretical significance and application prospects.

Key words: quantum, decision-making, equate-to-differentiate, disjunction effect, prisoner’s dilemma;

中图分类号:

B841.2
C934

辛潇洋, 李瑛, 毕研玲, 晏碧华. (2019). 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. 心理学报, 51(6), 724-733.

XIN Xiaoyang, LI Ying, BI Yanling, YAN Bihua. (2019). Quantum decision-making model based on equate-to-differentiate method: Explanation for the disjunction effect in prisoner’s dilemma. Acta Psychologica Sinica, 51(6), 724-733.

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

图1 Pothos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

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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