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Acta Psychologica Sinica    2019, Vol. 51 Issue (6) : 724-733     DOI: 10.3724/SP.J.1041.2019.00724
Reports of Empirical Studies |
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
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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.

Keywords quantum      decision-making      equate-to-differentiate      disjunction effect      prisoner’s dilemma;     
ZTFLH:  B841.2  
  C934  
Corresponding Authors: Ying LI     E-mail: liying@snnu.edu.cn
Issue Date: 25 April 2019
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Xiaoyang XIN
Ying LI
Yanling BI
Bihua YAN
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Xiaoyang XIN,Ying LI,Yanling BI, et al. Quantum decision-making model based on equate-to-differentiate method: Explanation for the disjunction effect in prisoner’s dilemma[J]. Acta Psychologica Sinica, 2019, 51(6): 724-733.
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http://journal.psych.ac.cn/xlxb/EN/10.3724/SP.J.1041.2019.00724     OR     http://journal.psych.ac.cn/xlxb/EN/Y2019/V51/I6/724
策略 你选择背叛 你选择合作
对方背叛 你:πa 对方:πa 你:πb 对方:πc
对方合作 你:πc 对方:πb 你:πd 对方:πd
  
  
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
  
  
  
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