禀赋效应和自然产权的演化:一个主体基模型
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摘要
禀赋效应从何而来,又如何与自然产权协同演化,这些问题尚未获得充分研究。本文提出一个"偏好演化+个体选择"的主体基模型(agent-based model),发现在非常广泛的参数空间内,均可涌现出稳健的禀赋效应和自然产权现象:绝大部分实验世界都由具有禀赋效应的个体所占据;产权尊重是常态,战争和掠夺的概率微乎其微。这一切源于:在自然选择压力下,个体对物品或资源在拥有时主观评价过高,而在不拥有时主观评价趋近客观真实价值,这种具有禀赋效应的偏好有利于遏制其他个体对其拥有物的抢夺,因而这种看似"错误"的偏好反而改善了主体的处境,使得禀赋效应得以成功演化。本文还发现,优质资源的稀缺程度会影响禀赋效应的演化速度和水平。上述发现可为自发秩序的制度经济分析奠定更坚实的理论基础。
The existent literature suggests that the endowment effect is essential for the formation of natural property rights. However, where the endowment effect comes from and how it coevolves with natural property rights is not fully understood. This paper develops an agent-based model featuring "preference evolution + individual choice" to examine how the endowment effect could be shaped and how natural property rights could emerge in an evolutionary artificial society. In our agent-based model, each agent has a pair of preference genes that respectively determine its subjective valuations of the resources it owns or does not own. The agent's subjective evaluation of resources may be biased or deviate from the true value of the resource, which is defined as the survival value, i.e., how much benefit the resources objectively bring to the agent for her survival. Each agent can only survive for a single period, during which some agents will randomly become the owner of a resource(i.e., the incumbent), and other unlucky agents become wanderers without any resources. The wanderer needs to decide whether to launch a fight to seize resources from the incumbent. Whether or not a fight breaks out, the agents' interaction will determine how many resources each party can obtain, and thus the number of descendants the agent can produce. At the end of a period, all agents will die, and their descendants will repeat their stories. Each descendant inherits the gene from its parent; that is, an agent's subjective valuation of the resource in both owned and unowned states will be the same as that of its parent. When the model is run, the results show that the emergence of the endowment effect is typically evolutionarily stable, i.e., a higher valuation of an owned resource and a lower valuation of an unowned resource is an evolutionarily stable result. With massive simulation experiments, we determined that the endowment effect coefficient(measured by the ratio of subjective valuations of resources when owned and not owned) is around 1.6, and in 90% of the experiments it is in the interval [1, 2.5], which is quite close to the endowment effect coefficients found in 169 behavioral experiments in the 39 projects surveyed by Sayman & Öncüler(2005). The experimental results of our agent-based model are thus consistent with the WTA/WTP deviation observed in a large number of experimental studies. We also found that the relative value of resources affects the evolution rate and the level of the endowment effect, but has no effect on whether the endowment effect occurs.Furthermore, we found that agents' subjective valuation of unowned resources tends to approach the true value(i.e., survival value) of the resources when the evolution process is long enough, while the agents' subjective valuation of owned resources is always higher than the true value of the resources, even over a very long process of evolution. These results show that the agents' valuation is closer to the objective value for unowned resources while higher than the objective value for owned resources. The reason is that the excessive valuation of a possession makes an agent more able to defend it from being snatched away, so this seemingly "wrong" preference improves the agent's situation and thus makes the endowment effect more likely to evolve successfully as a psychological tendency. Once the endowment effect emerges in the evolutionary process, an agent with this psychological tendency has a solid commitment mechanism, which makes the agent credibly "more willing to pay for the defense of possessions",and thus others are discouraged from stealing them from the agent. When the robbing intentions of other agents are completely inhibited, natural property rights, or spontaneous respect for property rights, will be pervasive in a given society. This paper not only provides an evolutionary explanation for the origin of the endowment effect, but also provides a theoretical logic and computer simulation evidence for the co-evolution of the endowment effect and natural property rights. Our model disposes of the troubles and confusions resulting from the fact that the property rights phenomenon and the anti-property phenomenon always have the same conditions and the same possibilities; this difficulty has long vexed the classic literature such as Smith(1982) and Gintis(2007, 2009). Thus our approach provides a more solid theoretical foundation for the institutional economic analysis of spontaneous order.
The existent literature suggests that the endowment effect is essential for the formation of natural property rights. However, where the endowment effect comes from and how it coevolves with natural property rights is not fully understood. This paper develops an agent-based model featuring "preference evolution + individual choice" to examine how the endowment effect could be shaped and how natural property rights could emerge in an evolutionary artificial society. In our agent-based model, each agent has a pair of preference genes that respectively determine its subjective valuations of the resources it owns or does not own. The agent's subjective evaluation of resources may be biased or deviate from the true value of the resource, which is defined as the survival value, i.e., how much benefit the resources objectively bring to the agent for her survival. Each agent can only survive for a single period, during which some agents will randomly become the owner of a resource(i.e., the incumbent), and other unlucky agents become wanderers without any resources. The wanderer needs to decide whether to launch a fight to seize resources from the incumbent. Whether or not a fight breaks out, the agents' interaction will determine how many resources each party can obtain, and thus the number of descendants the agent can produce. At the end of a period, all agents will die, and their descendants will repeat their stories. Each descendant inherits the gene from its parent; that is, an agent's subjective valuation of the resource in both owned and unowned states will be the same as that of its parent. When the model is run, the results show that the emergence of the endowment effect is typically evolutionarily stable, i.e., a higher valuation of an owned resource and a lower valuation of an unowned resource is an evolutionarily stable result. With massive simulation experiments, we determined that the endowment effect coefficient(measured by the ratio of subjective valuations of resources when owned and not owned) is around 1.6, and in 90% of the experiments it is in the interval [1, 2.5], which is quite close to the endowment effect coefficients found in 169 behavioral experiments in the 39 projects surveyed by Sayman & Öncüler(2005). The experimental results of our agent-based model are thus consistent with the WTA/WTP deviation observed in a large number of experimental studies. We also found that the relative value of resources affects the evolution rate and the level of the endowment effect, but has no effect on whether the endowment effect occurs.Furthermore, we found that agents' subjective valuation of unowned resources tends to approach the true value(i.e., survival value) of the resources when the evolution process is long enough, while the agents' subjective valuation of owned resources is always higher than the true value of the resources, even over a very long process of evolution. These results show that the agents' valuation is closer to the objective value for unowned resources while higher than the objective value for owned resources. The reason is that the excessive valuation of a possession makes an agent more able to defend it from being snatched away, so this seemingly "wrong" preference improves the agent's situation and thus makes the endowment effect more likely to evolve successfully as a psychological tendency. Once the endowment effect emerges in the evolutionary process, an agent with this psychological tendency has a solid commitment mechanism, which makes the agent credibly "more willing to pay for the defense of possessions",and thus others are discouraged from stealing them from the agent. When the robbing intentions of other agents are completely inhibited, natural property rights, or spontaneous respect for property rights, will be pervasive in a given society. This paper not only provides an evolutionary explanation for the origin of the endowment effect, but also provides a theoretical logic and computer simulation evidence for the co-evolution of the endowment effect and natural property rights. Our model disposes of the troubles and confusions resulting from the fact that the property rights phenomenon and the anti-property phenomenon always have the same conditions and the same possibilities; this difficulty has long vexed the classic literature such as Smith(1982) and Gintis(2007, 2009). Thus our approach provides a more solid theoretical foundation for the institutional economic analysis of spontaneous order.
引文
董志强,2011:《我们为何偏好公平:一个演化视角的解释》,《经济研究》第8期。
董志强、张永璟,2016:《禀赋效应与自发社会秩序:一个行为经济理论》,《世界经济》第10期。
黄凯南,2010:《主观博弈论与制度内生演化》,《经济研究》第4期。
牛贺,2017:《有限理性、规范内化与利他行为:一个演化视角》,《经济研究》第10期。
叶航,2012:《公共合作中的社会困境与社会正义——基于计算机仿真的经济学跨学科研究》,《经济研究》第8期。
Apicella, C. L., M. A. Eduardo, A. C. Nicholas, and H. F. James, 2014, “Evolutionary Origins of the Endowment Effect: Evidence from Hunter-Gatherers”, American Economic Review, 104(6), 1793—1805.
Camerer, C., and G. Loewenstein, 2004, “Behavioral Economics: Past, Present, Future”, in Camerer, C., Loewenstein, G., and Rabin, M. (ed.), Advances in Behavioral Economics, NJ: Princeton University Press,3—52.
Camerer, C., G. Loewenstein, and D. Prelec, 2005,“Neuroeconomics: How Neuroscience can Inform Economics”, Journal of Economic Literature, 43(1), 9—64.
Davies, N. B., 1978, “Territorial Defence in the Speckled Wood Butterfly (Pararge aegeria): The Resident Always Wins”, Animal Behaviour, 26, 138—147.
Dixit, A., 1987, “Strategic Behavior in Contests”, American Economic Review,77(5), 891—898.
Dong, Z., and Y. Zhang, 2016, “A Sequential Game of Endowment Effect and Natural Property Rights”, Economics Letters, 149, 108—111.
Eason, P. K., G. A. Cobbs, and K. G. Trinca, 1999, “The Use of Landmarks to Define Territorial Boundaries”, Animal Behaviour, 58(1), 85—91.
Ellis, L., 1985, “On the Rudiments of Possessions and Property”, Social Science Information, 24(1), 113—143.
Eswaran, M., and H. M.Neary, 2014, “An Economic Theory of the Evolutionary Emergence of Property Rights”, American Economic Journal: Microeconomics, 6(3), 203—226.
Frenkel, S., Y. Heller, and R. Teper, 2018, “The Endowment Effect as Blessing”, International Economic Review, 59(3), 1159—1186.
Fryer Jr, R. G., S. D. Levitt, J. List, and S. Sadoff, 2012, “Enhancing the Efficacy of Teacher Incentives through Loss Aversion: A Field Experiment”, National Bureau of Economic Research, No. W18237.
Genesove, D., and C. Mayer, 2001, “Loss Aversion and Seller Behavior: Evidence from the Housing Market”, Quarterly Journal of Economics, 116(4), 1233—1260.
Gintis, H., 2007, “The Evolution of Private Property”, Journal of Economic Behavior and Organization, 64(1), 1—16.
Gintis, H., 2009, The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences, NJ: Princeton University Press.
Harbaugh, W. T., K. Krause, and L. Vesterlund, 2001, “Are Adults Better Behaved than Children? Age, Experience, and the Endowment Effect”, Economics Letters, 70(2), 175—181.
Horowitz, J. K., and K. E. Mcconnell, 2002, “A Review of WTA/WTP Studies”, Journal of Environmental Economics and Management, 3(44), 426—447.
Hossain, T., and J. A. List, 2012, “The Behavioralist Visits the Factory: Increasing Productivity Using Simple Framing Manipulations”, Management Science, 58(12), 2151—2167.
Huck, S., G. Kirchsteiger, and J. Oechssler, 2005, “Learning to Like What You Have-explaining the Endowment Effect”, Economic Journal, 115, 689—702.
Johnes, O. D., 2001, “Time-Shifted Rationality and the Law of Law’s Leverage: Behavioral Economics Meets Behavioral Biology”, Northwestern University Law Review, 95, 1141—1206.
Jones, O. D., and S. F. Brosnan, 2008, “Law, Biology, and Property: A New Theory of the Endowment Effect”, William and Mary Law Review, 49(6), 1935—1990.
Kahneman, D., J. L. Knetsch, R. H. Thaler, H. Johnson, and L. Professor, 1991, “Anomalies: the Endowment Effect, Loss Aversion, and Status Quo Bias Anomalies the Endowment Effect, Loss Aversion, and Status Quo Bias”, Journal of Economic Perspectives, 5(1), 193— 206.
List, J. A., 2004a, “Neoclassical Theory Versus Prospect Theory: Evidence from the Marketpla”, Econometrica, 72(2), 615—625.
List, J. A., 2004b, “Substitutability, Experience, and the Value Disparity: Evidence from the marketplace”, Journal of Environmental Economics and Management, 47(3), 486—509.
Mesterton-Gibbons, M., 1992, “Ecotypic Variation in the Asymmetric Hawk-Dove Game: When is Bourgeois an Evolutionarily Stable Strategy?”, Evolutionary Ecology, 6(3), 198—222.
Plott, C. R., and K. Zeiler, 2007, “Exchange Asymmetries Incorrectly Interpreted as Evidence of Endowment Effect Theory and Prospect Theory”, American Economic Review, 97(4), 1449—1466.
Rand, A. S., 1967, “Ecology and Social Organization in the Iguanid Lizard Anolis Lineatopus”, Proceedings of the United States National Museum, 122, 1—79.
Riechert, S. E., 1978, “Games Spiders Play: Behavioral Variability in Territorial Disputes”, Behavioral Ecology and Sociobiology, 3(2), 135—162.
Sayman,S., and A. ?ncüler, 2005, “Effects of Study Design Characteristics on the WTA-WTP Disparity: A Meta Analytical Framework”, Journal of Economic Psychology, 26(2): 289—312.
Senar, J. C., M. Camerino, and N. B. Metcalfe, 1989, “Agonistic Interactions in Siskin Flocks: Why are Dominants Sometimes Subordinate?”, Behavioral Ecology and Sociobiology, 25(2), 141—145.
Smith, J. M., 1978, Models in Ecology, USA: Cambridge University Press.
Smith, J. M., 1982, Evolution and the Theory of Games. USA: Cambridge University Press.
Smith, J. M., and G. R. Price,1973, “The Logic of Animal Conflict”, Nature, 246, 15—18.
Stake, J. E., 2004, “The Property Instinct”, Philosophical Transactions of the Royal Society of London B, 359, 1763—1774.
Stevens, E. F.,1988, “Contests Between Bands of Feral Horses For Access to Fresh Water: The Resident Wins”, Animal Behaviour, 36(6), 1851—1853.
Tuncel, T., and J. K. Hammitt, 2014, “A New Meta-Analysis on the WTP/WTA Disparity”, Journal of Environmental Economics and Management, 68(1), 175—187.
Tversky, A., and D. Kahneman, 1991, “Loss Aversion in Riskless Choice: A Reference-dependent Model”, Quarterly Journal of Economics, 106(4), 1039—1061.
Van Boven, L., G. Loewenstein, and D. Dunning, 2003, “Mispredicting the Endowment Effect: Underestimation of Owners’ Selling Prices by Buyer’s Agents”, Journal of Economic Behavior and Organization, 51(3), 351—365.
Wilkinson, N., and M. Klaes,2012, “An Introduction to Behavioral Economics”, Palgrave Macmillan.
① 自然产权是自然财产权利(natural property right)的简称,顾名思义,是一种自然而然的产权。它无须依赖第三方力量,可以在行为主体之间自我实施。本质上,自然产权可以视为对他人权利的自发尊重。我们要研究的自然产权,并非自然资源产权(natural resources property),后者是一个法律术语,指的是对山川土地河流等自然资源的所有权。自然产权多见于经济学和哲学论著中,是自然权利(natural rights)之一种。
(1)恃强凌弱在人类社会并不普遍,甚至在动物社会也没我们想象的那么多(Gintis,2009)。
(2)对于人类,做出一种捍卫地盘的宣誓就是一个信号;对于动物,利用声音、威胁动作等都是信号。这里,假设信号是可信的承诺,不考虑发送虚假信号的问题,以尽量简化模型。
(3)本文模型允许以0成本发起战斗,相当于装腔作势虚晃一枪,若不能吓倒对手则立即撤退。
(4)应注意到,图1(b)中,震慑区的边界是,其斜率可以大于45度线,因此一直延长该边界必定与45度线有交点,从而导致震慑区有可能向左上越过45线(进入不存在禀赋效应的区域)。但是,这样的结果仅存在于β2<β1/2的情形。在长期演化中,β2<β1/2不可能是演化稳定状态,因此产权尊重就只会出现在禀赋效应区域。
(5)初始财富禀赋是为了尽量避免“负赢利的适存性”问题。可参阅Smith(1982)。
(6)Wilensky, U.,1999, NetLogo. http://ccl.northwestern.edu/netlogo/,Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
(7)R Core Team,2013, R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.
(8)成语“完璧归赵”所记录的一个情节堪称“玉碎”策略的典型例子:秦昭王意图抢夺和氏璧,蔺相如的策略是,如果秦昭王逼他,他就把头和璧一起撞到柱子上(让秦昭王不可能得到和氏璧)。
董志强、张永璟,2016:《禀赋效应与自发社会秩序:一个行为经济理论》,《世界经济》第10期。
黄凯南,2010:《主观博弈论与制度内生演化》,《经济研究》第4期。
牛贺,2017:《有限理性、规范内化与利他行为:一个演化视角》,《经济研究》第10期。
叶航,2012:《公共合作中的社会困境与社会正义——基于计算机仿真的经济学跨学科研究》,《经济研究》第8期。
Apicella, C. L., M. A. Eduardo, A. C. Nicholas, and H. F. James, 2014, “Evolutionary Origins of the Endowment Effect: Evidence from Hunter-Gatherers”, American Economic Review, 104(6), 1793—1805.
Camerer, C., and G. Loewenstein, 2004, “Behavioral Economics: Past, Present, Future”, in Camerer, C., Loewenstein, G., and Rabin, M. (ed.), Advances in Behavioral Economics, NJ: Princeton University Press,3—52.
Camerer, C., G. Loewenstein, and D. Prelec, 2005,“Neuroeconomics: How Neuroscience can Inform Economics”, Journal of Economic Literature, 43(1), 9—64.
Davies, N. B., 1978, “Territorial Defence in the Speckled Wood Butterfly (Pararge aegeria): The Resident Always Wins”, Animal Behaviour, 26, 138—147.
Dixit, A., 1987, “Strategic Behavior in Contests”, American Economic Review,77(5), 891—898.
Dong, Z., and Y. Zhang, 2016, “A Sequential Game of Endowment Effect and Natural Property Rights”, Economics Letters, 149, 108—111.
Eason, P. K., G. A. Cobbs, and K. G. Trinca, 1999, “The Use of Landmarks to Define Territorial Boundaries”, Animal Behaviour, 58(1), 85—91.
Ellis, L., 1985, “On the Rudiments of Possessions and Property”, Social Science Information, 24(1), 113—143.
Eswaran, M., and H. M.Neary, 2014, “An Economic Theory of the Evolutionary Emergence of Property Rights”, American Economic Journal: Microeconomics, 6(3), 203—226.
Frenkel, S., Y. Heller, and R. Teper, 2018, “The Endowment Effect as Blessing”, International Economic Review, 59(3), 1159—1186.
Fryer Jr, R. G., S. D. Levitt, J. List, and S. Sadoff, 2012, “Enhancing the Efficacy of Teacher Incentives through Loss Aversion: A Field Experiment”, National Bureau of Economic Research, No. W18237.
Genesove, D., and C. Mayer, 2001, “Loss Aversion and Seller Behavior: Evidence from the Housing Market”, Quarterly Journal of Economics, 116(4), 1233—1260.
Gintis, H., 2007, “The Evolution of Private Property”, Journal of Economic Behavior and Organization, 64(1), 1—16.
Gintis, H., 2009, The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences, NJ: Princeton University Press.
Harbaugh, W. T., K. Krause, and L. Vesterlund, 2001, “Are Adults Better Behaved than Children? Age, Experience, and the Endowment Effect”, Economics Letters, 70(2), 175—181.
Horowitz, J. K., and K. E. Mcconnell, 2002, “A Review of WTA/WTP Studies”, Journal of Environmental Economics and Management, 3(44), 426—447.
Hossain, T., and J. A. List, 2012, “The Behavioralist Visits the Factory: Increasing Productivity Using Simple Framing Manipulations”, Management Science, 58(12), 2151—2167.
Huck, S., G. Kirchsteiger, and J. Oechssler, 2005, “Learning to Like What You Have-explaining the Endowment Effect”, Economic Journal, 115, 689—702.
Johnes, O. D., 2001, “Time-Shifted Rationality and the Law of Law’s Leverage: Behavioral Economics Meets Behavioral Biology”, Northwestern University Law Review, 95, 1141—1206.
Jones, O. D., and S. F. Brosnan, 2008, “Law, Biology, and Property: A New Theory of the Endowment Effect”, William and Mary Law Review, 49(6), 1935—1990.
Kahneman, D., J. L. Knetsch, R. H. Thaler, H. Johnson, and L. Professor, 1991, “Anomalies: the Endowment Effect, Loss Aversion, and Status Quo Bias Anomalies the Endowment Effect, Loss Aversion, and Status Quo Bias”, Journal of Economic Perspectives, 5(1), 193— 206.
List, J. A., 2004a, “Neoclassical Theory Versus Prospect Theory: Evidence from the Marketpla”, Econometrica, 72(2), 615—625.
List, J. A., 2004b, “Substitutability, Experience, and the Value Disparity: Evidence from the marketplace”, Journal of Environmental Economics and Management, 47(3), 486—509.
Mesterton-Gibbons, M., 1992, “Ecotypic Variation in the Asymmetric Hawk-Dove Game: When is Bourgeois an Evolutionarily Stable Strategy?”, Evolutionary Ecology, 6(3), 198—222.
Plott, C. R., and K. Zeiler, 2007, “Exchange Asymmetries Incorrectly Interpreted as Evidence of Endowment Effect Theory and Prospect Theory”, American Economic Review, 97(4), 1449—1466.
Rand, A. S., 1967, “Ecology and Social Organization in the Iguanid Lizard Anolis Lineatopus”, Proceedings of the United States National Museum, 122, 1—79.
Riechert, S. E., 1978, “Games Spiders Play: Behavioral Variability in Territorial Disputes”, Behavioral Ecology and Sociobiology, 3(2), 135—162.
Sayman,S., and A. ?ncüler, 2005, “Effects of Study Design Characteristics on the WTA-WTP Disparity: A Meta Analytical Framework”, Journal of Economic Psychology, 26(2): 289—312.
Senar, J. C., M. Camerino, and N. B. Metcalfe, 1989, “Agonistic Interactions in Siskin Flocks: Why are Dominants Sometimes Subordinate?”, Behavioral Ecology and Sociobiology, 25(2), 141—145.
Smith, J. M., 1978, Models in Ecology, USA: Cambridge University Press.
Smith, J. M., 1982, Evolution and the Theory of Games. USA: Cambridge University Press.
Smith, J. M., and G. R. Price,1973, “The Logic of Animal Conflict”, Nature, 246, 15—18.
Stake, J. E., 2004, “The Property Instinct”, Philosophical Transactions of the Royal Society of London B, 359, 1763—1774.
Stevens, E. F.,1988, “Contests Between Bands of Feral Horses For Access to Fresh Water: The Resident Wins”, Animal Behaviour, 36(6), 1851—1853.
Tuncel, T., and J. K. Hammitt, 2014, “A New Meta-Analysis on the WTP/WTA Disparity”, Journal of Environmental Economics and Management, 68(1), 175—187.
Tversky, A., and D. Kahneman, 1991, “Loss Aversion in Riskless Choice: A Reference-dependent Model”, Quarterly Journal of Economics, 106(4), 1039—1061.
Van Boven, L., G. Loewenstein, and D. Dunning, 2003, “Mispredicting the Endowment Effect: Underestimation of Owners’ Selling Prices by Buyer’s Agents”, Journal of Economic Behavior and Organization, 51(3), 351—365.
Wilkinson, N., and M. Klaes,2012, “An Introduction to Behavioral Economics”, Palgrave Macmillan.
① 自然产权是自然财产权利(natural property right)的简称,顾名思义,是一种自然而然的产权。它无须依赖第三方力量,可以在行为主体之间自我实施。本质上,自然产权可以视为对他人权利的自发尊重。我们要研究的自然产权,并非自然资源产权(natural resources property),后者是一个法律术语,指的是对山川土地河流等自然资源的所有权。自然产权多见于经济学和哲学论著中,是自然权利(natural rights)之一种。
(1)恃强凌弱在人类社会并不普遍,甚至在动物社会也没我们想象的那么多(Gintis,2009)。
(2)对于人类,做出一种捍卫地盘的宣誓就是一个信号;对于动物,利用声音、威胁动作等都是信号。这里,假设信号是可信的承诺,不考虑发送虚假信号的问题,以尽量简化模型。
(3)本文模型允许以0成本发起战斗,相当于装腔作势虚晃一枪,若不能吓倒对手则立即撤退。
(4)应注意到,图1(b)中,震慑区的边界是,其斜率可以大于45度线,因此一直延长该边界必定与45度线有交点,从而导致震慑区有可能向左上越过45线(进入不存在禀赋效应的区域)。但是,这样的结果仅存在于β2<β1/2的情形。在长期演化中,β2<β1/2不可能是演化稳定状态,因此产权尊重就只会出现在禀赋效应区域。
(5)初始财富禀赋是为了尽量避免“负赢利的适存性”问题。可参阅Smith(1982)。
(6)Wilensky, U.,1999, NetLogo. http://ccl.northwestern.edu/netlogo/,Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
(7)R Core Team,2013, R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.
(8)成语“完璧归赵”所记录的一个情节堪称“玉碎”策略的典型例子:秦昭王意图抢夺和氏璧,蔺相如的策略是,如果秦昭王逼他,他就把头和璧一起撞到柱子上(让秦昭王不可能得到和氏璧)。