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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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。
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.
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.
引文
Baron,J.(2007).Thinking and deciding.Cambridge University Press.
Bi,Y.L.,Li,S.(2007).A comparison between two models of bounded rationality:Equate-to-differentiate and priority heuristic approaches.Advances in Psychological Science,15(4),682-688.[毕研玲,李纾.(2007).有限理性的"占优启发式"和"齐当别"决策模型的作为--当Allais悖论杠杆撬动了期望效用理论.心理科学进展,15(4),682-688.]
Blanco,M.,Engelmann,D.,Koch,A.K.,&Normann,H.T.(2014).Preferences and beliefs in a sequential social dilemma:A within-subjects analysis.Games and Economic Behavior,87,122-135.
Blutner,R.,Pothos,E.M.,&Bruza,P.(2013).A quantum probability perspective on borderline vagueness.Topics in Cognitive Science,5(4),711-736.
Bruza,P.D.,Wang,Z.,&Busemeyer,J.R.(2015).Quantum cognition:A new theoretical approach to psychology.Trends in Cognitive Sciences,19(7),383-393.
Busemeyer,J.R.,&Bruza,P.D.(2012).Quantum models of cognition and decision.Cambridge University Press.
Busemeyer,J.R.,&Johnson,J.G.(2008).Micro-process models of decision making.Cambridge Handbook of Computational Psychology.Cambridge University Press,(pp.302-321).
Busemeyer,J.R.,Matthew,M.R.,&Wang,Z.(2006).Aquantum information processing explanation of disjunction effects.Paper presented at the Proceedings of the Annual Meeting of the Cognitive Science Society.
Busemeyer,J.R.,&Townsend,J.T.(1993).Decision field theory:A dynamic-cognitive approach to decision making in an uncertain environment.Psychological Review,100(3),432-459.
Busemeyer,J.R.,&Wang,Z.(2015).What is quantum cognition,and how is it applied to psychology?Current Directions in Psychological Science,24(3),163-169.
Busemeyer,J.R.,Wang,Z.,Khrennikov,A.,&Basieva,I.(2014).Applying quantum principles to psychology.Physica Scripta,2014(T163),014007.
Busemeyer,J.R.,Wang,Z.,&Lambert-Mogiliansky,A.(2009).Empirical comparison of markov and quantum models of decision making.Journal of Mathematical Psychology,53(5),423-433.
Busemeyer,J.R.,Wang,Z.J.,&Pothos,E.(2015).Quantum models of cognition and decision.The Oxford Handbook of Computational and Mathematical Psychology.Oxford University Press,(pp.369-389).
Busemeyer,J.R.,Wang,Z.,&Townsend,J.T.(2006).Quantum dynamics of human decision-making.Journal of Mathematical Psychology,50(3),220-241.
Croson,R.T.A.(1999).The disjunction effect and reasonbased choice in games.Organizational Behavior and Human Decision Processes,80(2),118-133.
Denolf,J.,Martínez-Martínez,I.,Josephy,H.,&BarqueDuran,A.(2017).A quantum-like model for complementarity of preferences and beliefs in dilemma games.Journal of Mathematical Psychology,78,96-106.
Festinger,L.(1957).A theory of cognitive dissonance(Vol.2).Stanford university press.
Gigerenzer,G.,&Todd,P.M.(1999).Simple heuristics that make us smart.Oxford University Press.
Kahneman,D.,&Tversky,A.(2013).Prospect theory:An analysis of decision under risk.Handbook of the fundamentals of financial decision making:Part I(pp.99-127):World Scientific.
Kubovy,M.,Rapoport,A.,&Tversky,A.(1971).Deterministic vs probabilistic strategies in detection.Perception&Psychophysics,9(5),427-429.
Li,S.(2005).Choice reversals across certainty,uncertainty and risk:The equate-to-differentiate interpretation.Acta Psychologica Sinica,37(4),427-433.[李纾.(2005).确定、不确定及风险状态下选择反转:“齐当别”选择方式的解释.心理学报,37(4),427-433.]
Li,S.(2016).An equate-to-difference way of decision-making.Shanghai:East China Normal University Press.[李纾.(2016).决策心理:齐当别之道.上海:华东师范大学出版社.]
Li,S.,Bi,Y.L.,Liang Z.Y.,Sun,Y.,Wang,Z.J.,&Zheng,R.(2009).Bounded or unbounded rationality?The implication of equate-to-differentiate theory in economic behavior.Management Review,121(5),143-154.[李纾,毕研玲,梁竹苑,孙彦,汪祚军,郑蕊.(2009).无限理性还是有限理性?--齐当别抉择模型在经济行为中的应用.管理评论,121(5),143-154.]
Li,S,&Taplin,J.(2002).Examining whether there is a disjunction effect in prisoner's dilemma games.Chinese Journal of Psychology,44(1),25-46.
Li,S.,Taplin,J.E.,&Zhang,Y.C.(2007).The equate-todifferentiate’s way of seeing the prisoner’s dilemma.Information Sciences,177(6),1395-1412.
Payne,J.W.,&Bettman,J.R.(2004).Walking with the scarecrow:The information-processing approach to decision research.Blackwell Handbook of Judgment and Decision Making,110-132.
Pleskac,T.J.,Diederich,A.,&Wallsten,T.S.(2015).Models of decision making under risk and uncertainty.The Oxford handbook of computational and mathematical psychology.Oxford University Press,(pp.209-231).
Pothos,E.M.,&Busemeyer,J.R.(2009).A quantum probability explanation for violations of‘rational’decision theory.Proceedings of the Royal Society of London B:Biological Sciences,276(1665),2171-2178
Savage L J.(1954).The Foundations of Statistics.New York:Wiley.
Shafir,E.,&Tversky,A.(1992).Thinking through uncertainty:Nonconsequential reasoning and choice.Cognitive Psychology,24(4),449-474.
Smith,J.M.(1982).Evolution and the Theory of Games.Cambridge University Press.
Stevenson,M.K.,Busemeyer,J.R.,&Naylor,J.C.(1990).Judgment and decision-making theory.Handbook of Industrial&Organizational Psychology.Consulting Psychologist Press.
Su,R.K.(2002)Quantum Mechanics(Second Edition).Higher Education Press[苏汝铿.(2002).量子力学-第2版.高等教育出版社.]
Townsend,J.T.,Silva,K.M.,Spencer-Smith,J.,&Wenger,M.J.(2000).Exploring the relations between categorization and decision making with regard to realistic face stimuli.Pragmatics&Cognition,8(1),83-105.
Tversky,A.,&Kahneman,D.(1974).Judgment under uncertainty:Heuristics and biases.Science,185(4157),1124-1131.
Tversky,A.,&Kahneman,D.(1981).The framing of decisions and the psychology of choice.Science,211(4481),453-458.
Tversky,A.,&Shafir,E.(1992).The disjunction effect in choice under uncertainty.Psychological Science,3(5),305-310.
Wang,Z.,&Busemeyer,J.R.(2016).Interference effects of categorization on decision making.Cognition,150,133-149.
Wang,Z.J.,Li,S.(2008).The disjunction effect in decision making.Advances in Psychological Science,16(4),513-517.[汪祚军,李纾.(2008).行为决策中出现的分离效应.心理科学进展,16(4),513-517.]
Xin,X.Y.,Xu,C.H.,Chen,H.Y.,Li,Y.(2018).Quantum models for decision making.Advances in Psychological Science,26(8),1365-1373.[辛潇洋,徐晨虹,陈宏玉,李瑛.(2018).一种新决策模型--量子决策模型.心理科学进展,26(8),1365-1373.]
Yearsley,J.M.(2017).Advanced tools and concepts for quantum cognition:A tutorial.Journal of Mathematical Psychology,78,24-39.
1在量子决策模型中,通常将薛定谔方程中的普朗克常数h设定为1。方程中,i表示虚数单位,e表示自然常数,t表示决策过程所需的时间,但并非客观的绝对时间。
2仿照Pothos和Busemeyer(2009)中的图1,将分离效应量定义为决策者在不确定条件下选择背叛的概率减去两种确定情况下选择背叛概率的平均值,即:p(背叛)-1/2(p(背叛│对手合作))+p(背叛│对手背叛)。
3即ni→ni+?n自己收益维度下i={a,c};他人收益维度下i={c, d}。
Bi,Y.L.,Li,S.(2007).A comparison between two models of bounded rationality:Equate-to-differentiate and priority heuristic approaches.Advances in Psychological Science,15(4),682-688.[毕研玲,李纾.(2007).有限理性的"占优启发式"和"齐当别"决策模型的作为--当Allais悖论杠杆撬动了期望效用理论.心理科学进展,15(4),682-688.]
Blanco,M.,Engelmann,D.,Koch,A.K.,&Normann,H.T.(2014).Preferences and beliefs in a sequential social dilemma:A within-subjects analysis.Games and Economic Behavior,87,122-135.
Blutner,R.,Pothos,E.M.,&Bruza,P.(2013).A quantum probability perspective on borderline vagueness.Topics in Cognitive Science,5(4),711-736.
Bruza,P.D.,Wang,Z.,&Busemeyer,J.R.(2015).Quantum cognition:A new theoretical approach to psychology.Trends in Cognitive Sciences,19(7),383-393.
Busemeyer,J.R.,&Bruza,P.D.(2012).Quantum models of cognition and decision.Cambridge University Press.
Busemeyer,J.R.,&Johnson,J.G.(2008).Micro-process models of decision making.Cambridge Handbook of Computational Psychology.Cambridge University Press,(pp.302-321).
Busemeyer,J.R.,Matthew,M.R.,&Wang,Z.(2006).Aquantum information processing explanation of disjunction effects.Paper presented at the Proceedings of the Annual Meeting of the Cognitive Science Society.
Busemeyer,J.R.,&Townsend,J.T.(1993).Decision field theory:A dynamic-cognitive approach to decision making in an uncertain environment.Psychological Review,100(3),432-459.
Busemeyer,J.R.,&Wang,Z.(2015).What is quantum cognition,and how is it applied to psychology?Current Directions in Psychological Science,24(3),163-169.
Busemeyer,J.R.,Wang,Z.,Khrennikov,A.,&Basieva,I.(2014).Applying quantum principles to psychology.Physica Scripta,2014(T163),014007.
Busemeyer,J.R.,Wang,Z.,&Lambert-Mogiliansky,A.(2009).Empirical comparison of markov and quantum models of decision making.Journal of Mathematical Psychology,53(5),423-433.
Busemeyer,J.R.,Wang,Z.J.,&Pothos,E.(2015).Quantum models of cognition and decision.The Oxford Handbook of Computational and Mathematical Psychology.Oxford University Press,(pp.369-389).
Busemeyer,J.R.,Wang,Z.,&Townsend,J.T.(2006).Quantum dynamics of human decision-making.Journal of Mathematical Psychology,50(3),220-241.
Croson,R.T.A.(1999).The disjunction effect and reasonbased choice in games.Organizational Behavior and Human Decision Processes,80(2),118-133.
Denolf,J.,Martínez-Martínez,I.,Josephy,H.,&BarqueDuran,A.(2017).A quantum-like model for complementarity of preferences and beliefs in dilemma games.Journal of Mathematical Psychology,78,96-106.
Festinger,L.(1957).A theory of cognitive dissonance(Vol.2).Stanford university press.
Gigerenzer,G.,&Todd,P.M.(1999).Simple heuristics that make us smart.Oxford University Press.
Kahneman,D.,&Tversky,A.(2013).Prospect theory:An analysis of decision under risk.Handbook of the fundamentals of financial decision making:Part I(pp.99-127):World Scientific.
Kubovy,M.,Rapoport,A.,&Tversky,A.(1971).Deterministic vs probabilistic strategies in detection.Perception&Psychophysics,9(5),427-429.
Li,S.(2005).Choice reversals across certainty,uncertainty and risk:The equate-to-differentiate interpretation.Acta Psychologica Sinica,37(4),427-433.[李纾.(2005).确定、不确定及风险状态下选择反转:“齐当别”选择方式的解释.心理学报,37(4),427-433.]
Li,S.(2016).An equate-to-difference way of decision-making.Shanghai:East China Normal University Press.[李纾.(2016).决策心理:齐当别之道.上海:华东师范大学出版社.]
Li,S.,Bi,Y.L.,Liang Z.Y.,Sun,Y.,Wang,Z.J.,&Zheng,R.(2009).Bounded or unbounded rationality?The implication of equate-to-differentiate theory in economic behavior.Management Review,121(5),143-154.[李纾,毕研玲,梁竹苑,孙彦,汪祚军,郑蕊.(2009).无限理性还是有限理性?--齐当别抉择模型在经济行为中的应用.管理评论,121(5),143-154.]
Li,S,&Taplin,J.(2002).Examining whether there is a disjunction effect in prisoner's dilemma games.Chinese Journal of Psychology,44(1),25-46.
Li,S.,Taplin,J.E.,&Zhang,Y.C.(2007).The equate-todifferentiate’s way of seeing the prisoner’s dilemma.Information Sciences,177(6),1395-1412.
Payne,J.W.,&Bettman,J.R.(2004).Walking with the scarecrow:The information-processing approach to decision research.Blackwell Handbook of Judgment and Decision Making,110-132.
Pleskac,T.J.,Diederich,A.,&Wallsten,T.S.(2015).Models of decision making under risk and uncertainty.The Oxford handbook of computational and mathematical psychology.Oxford University Press,(pp.209-231).
Pothos,E.M.,&Busemeyer,J.R.(2009).A quantum probability explanation for violations of‘rational’decision theory.Proceedings of the Royal Society of London B:Biological Sciences,276(1665),2171-2178
Savage L J.(1954).The Foundations of Statistics.New York:Wiley.
Shafir,E.,&Tversky,A.(1992).Thinking through uncertainty:Nonconsequential reasoning and choice.Cognitive Psychology,24(4),449-474.
Smith,J.M.(1982).Evolution and the Theory of Games.Cambridge University Press.
Stevenson,M.K.,Busemeyer,J.R.,&Naylor,J.C.(1990).Judgment and decision-making theory.Handbook of Industrial&Organizational Psychology.Consulting Psychologist Press.
Su,R.K.(2002)Quantum Mechanics(Second Edition).Higher Education Press[苏汝铿.(2002).量子力学-第2版.高等教育出版社.]
Townsend,J.T.,Silva,K.M.,Spencer-Smith,J.,&Wenger,M.J.(2000).Exploring the relations between categorization and decision making with regard to realistic face stimuli.Pragmatics&Cognition,8(1),83-105.
Tversky,A.,&Kahneman,D.(1974).Judgment under uncertainty:Heuristics and biases.Science,185(4157),1124-1131.
Tversky,A.,&Kahneman,D.(1981).The framing of decisions and the psychology of choice.Science,211(4481),453-458.
Tversky,A.,&Shafir,E.(1992).The disjunction effect in choice under uncertainty.Psychological Science,3(5),305-310.
Wang,Z.,&Busemeyer,J.R.(2016).Interference effects of categorization on decision making.Cognition,150,133-149.
Wang,Z.J.,Li,S.(2008).The disjunction effect in decision making.Advances in Psychological Science,16(4),513-517.[汪祚军,李纾.(2008).行为决策中出现的分离效应.心理科学进展,16(4),513-517.]
Xin,X.Y.,Xu,C.H.,Chen,H.Y.,Li,Y.(2018).Quantum models for decision making.Advances in Psychological Science,26(8),1365-1373.[辛潇洋,徐晨虹,陈宏玉,李瑛.(2018).一种新决策模型--量子决策模型.心理科学进展,26(8),1365-1373.]
Yearsley,J.M.(2017).Advanced tools and concepts for quantum cognition:A tutorial.Journal of Mathematical Psychology,78,24-39.
1在量子决策模型中,通常将薛定谔方程中的普朗克常数h设定为1。方程中,i表示虚数单位,e表示自然常数,t表示决策过程所需的时间,但并非客观的绝对时间。
2仿照Pothos和Busemeyer(2009)中的图1,将分离效应量定义为决策者在不确定条件下选择背叛的概率减去两种确定情况下选择背叛概率的平均值,即:p(背叛)-1/2(p(背叛│对手合作))+p(背叛│对手背叛)。
3即ni→ni+?n自己收益维度下i={a,c};他人收益维度下i={c, d}。