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inverse-S: suggest that their data for probability transf. agree with Preston & Baratta’s but this is not much so. Sprowls (1953) says they are more variable. P. 397: for Preston & Baratta probability transformation (assuming linear utility) intersects the diagonal at about 0.2, in this experiment at 0.5 for guardsmen, and not for the students (they are always risk averse). Domain: [0.05, 5.50] P. 398 has nice discussion of problem with transforming fixed probabilities, that they must violate transitivity and do not sum to one. (biseparable utility) Then also, nicely, for two-outcome gambles, that subjects focus on a particular outcome, and let the other outcome have rest of unitary decision weight. This would be biseparable utility (RDU for two outcomes) if the particular outcome were always the best, or always the worst. Point out that for more than two outcomes the formula then is not clear. SEU = SEU: p. 398 has good discussion, with footnote 16 pointing out that additive subjective probabilities if unequal to objective probabilities cannot be transforms of the latter. P. 402, §VI.E: utility of gambling. %} Mosteller, Frederick & Philip Nogee (1951) “An Experimental Measurement of Utility,” Journal of Political Economy 59, 371–404. {% %} Moulin, Hervé (1985) “Egalitarianism and Utilitarianism in Quasi-Linear Bargaining,” Econometrica 53, 49–68. {% %} Moulin, Hervé (1987) “Equal or Proportional Division of a Surplus, and Other Methods,” International Journal of Game Theory 16, 161–186. {% %} Moulin, Hervé (1988) “Axioms of Cooperative Decision Making.” Cambridge University Press, New York. {% %} Mowen, John C. & James W. Gentry (1980) “Investigation of the Preference-Reversal Phenomenon in a New Product Introduction Task,” Journal of Applied Psychology 65, 715–722. {% %} Mowrer, O. Hobart & Lawrence N. Solomon (1954) “Contiguity vs Drive-Reduction in Conditioned Fear: The Proximity and Abrubtness of Drive-Reduction,” American Journal of Psychology 67, 15–25. {% %} Moyes, Patrick (2007) “An Extended Gini Approach to Inequality Measurement,” Journal of Economic Inequality 5, 279–303. {% %} Muermann, Alexander, Olivia S. Mitchell, & Jacqueline M. Volkman (2006) “Regret, Portfolio Choice, and Guarantees in Defined Contribution Schemes,” Insurance: Mathematics and Economics 39, 219–229. {% Application of ambiguity theory; Measure ambiguity aversion in the traditional way, with choices between gambles on known/unknown urns, some hypothetical and some with real incentives (RIS). Ambiguity aversion is correlated with preference for known brand (not very surprising given that both concern a preference for known versus unknown). The effect is enhanced if ambiguity aversion is enhanced by a lottery choice prior to the brand choice (priming). %} Muthukrishnan, Analmalal V., Luc Wathieu, & Alison Jing Xu (2009) “Ambiguity Aversion and the Preference for Established Brands,” Managent Science 55, 1933–1941. {% %} Müller, Werner G., Antonio C.M. Ponce De Leon (1996) “Optimal Design of an Experiment in Economics,” Economic Journal 106, 122–127. {% %} Müller-Peters, Anke (1998) “The Significance of National Pride and National Identity to the Attitude toward the Single European Currency: A Europe-Wide Comparison,” Journal of Economic Psychology 19, 701–719. {% Describes ideas of belief functions; updating, giving new interpretation of Dempster/Shafer updating; small worlds: uses incomplete state spaces as argument, adds one catch all state. %} Mukerji, Sujoy (1997) “Understanding the Nonadditive Probability Decision Model,” Economic Theory 9, 23–46. {% Application of ambiguity theory; PT, applications: nonadditive measures, incomplete markets. Uses Choquet expected utility with convex weighting function. %} Mukerji, Sujoy (1998) “Ambiguity Aversion and Incompleteness of Contractual Form,” American Economic Review 88, 1207–1231. {% %} Mukerji, Sujoy (2003) Book Review of: Ellsberg, Daniel (2001) “Risk, Ambiguity and Decision,” Garland Publishers, New York,” Economic Journal 113, 187–188. {% %} Mukerji, Sujoy (2009) “Foundations of Ambiguity and Economic Modeling,” Economics and Philosophy 25, 297–302. {% Application of ambiguity theory; PT, applications: nonadditive measures, incomplete markets; equilibrium under nonEU: general equilibrium with incomplete markets explained using Choquet expected utility with convex capacity %} Mukerji, Sujoy & Jean-Marc Tallon (2001) “Ambiguity Aversion and Incompleteness of Financial Markets,” Review of Economic Studies 68, 883–904. {% Portfolio inertia: there is an interval of prices at which an agent strictly prefers zero position on an asset. This is related to partition-wise preference as in source preference of Tversky & Wakker (1995). As often, the authors throughout equate ambiguity attitude with ambiguity aversion. So, source preference for A over B, in absence of ambiguity seeking for A, must then mean ambiguity aversion for B. Proposition 3.a shows that, if source preference for {A1,A2} over {B1,B2}, then A1 B1 or A2 B2 must be ambiguous in sense of Epstein & Zhang (2001) by simple natural proof. Proposition 1 is corrected by Higashi, Mukerji, Takeoka, & Tallon (2008), %} Mukerji, Sujoy & Jean-Marc Tallon (2003) “Ellsberg’s Two-Color Experiment, Portfolio Inertia and Ambiguity,” Journal of Mathematical Economics 39, 299–315. {% Absence of indexation of loans is explained through multiple priors/Choquet expected utility with convex capacity. %} Mukerji, Sujoy & Jean-Marc Tallon (2004) “Ambiguity Aversion and the Absence of Indexed Debt,” Economic Theory 24, 665–685. {% Use Choquet expected utility to analyze the topic of their title. %} Mukerji, Sujoy & Jean-Marc Tallon (2004) “Ambiguity Aversion and the Absence of Wage Indexation,” Journal of Monetary Economics 51, 653–670. {% %} Mukerji, Sujoy & Jean-Marc Tallon (2004) “An Overview of Economic Applications of David Schmeidler’s Models of Decision Making under Uncertainty.” In Itzhak Gilboa (ed.) Uncertainty in Economic Theory: Essays in Honor of David Schmeidler’s 65th Birthday, Routledge, London. {% Cognitive interpretation of inverse-S: the more emotionally people think (measured using questionnaires), the more inverse-S probability weighting (cognitive ability related to likelihood insensitivity (= inverse-S)). Although the author several times refers to the relevance of utility curvature, probability weighting is measured assuming linear utility, which is reasonable for moderate amounts but could have been mentioned. The author, rightfully, points out that besides curvature also elevation is relevant. %} Mukherjee, Kanchan (2011) “Thinking Styles and Risky Decision-Making: Further Exploration of the Affect–Probability Weighting Link,” Journal of Behavioral Decision Making 24, 443–455. {% Consider introspective judgments of value of money and relate it to loss aversion. When glancing through the paper I did not see the hypothesis mentioned that loss aversion is due, not to losses being more intense experiences than gains, but losses being weighted more, but I may have missed it. They find no clear results and end the abstract with psychologists’ favorite conclusion of context dependence: “Prospect Theory’s value function is contextually dependent on magnitudes.” %} Mukherjee, Sumitava, Arvind Sahay, V. S. Chandrasekhar Pammi, & Narayanan Srinivasan (2017) “Is Loss-Aversion Magnitude-Dependent? Measuring Prospective Affective Judgments Regarding Gains and Losses,” Judgment and Decision Making 12, 81–89. {% Historical review of early works of de Finetti etc. %} Muliere, Pietro & Giovanni Parmigiani (1993) “Utility and Means in the 1930s,” Statistical Science 8, 421–432. {% Verbal text book on decision theory %} Mullen, John D. & Byron M. Roth (1991) “Decision Making, Its Logic and Practice.” Rowman & Littlefield, Savage Maryland. {% Do a multivariate generalization of decreasing differences to characterize more concave than. The authors’ term loss is not related to reference points or prospect theory or the like. In their terminology, under EU, fear of loss is equivalent to concave utility. %} Müller, Alfred & Marco Scarsini (2012) “Fear of Loss, Inframodularity, and Transfers,” Journal of Economic Theory 147, 1490–1500. {% %} Müller, Dennis C. (2003) “Public Choice III.” Cambridge University Press, Cambridge. {% foundations of probability %} Müller, Thomas (2005) “Probability Theory and Causation: A Branching Space-Times Analysis,” British Journal for the Philosophy of Science 56, 487–4520. {% %} Mulley, Albert G. (1989) “Assessing Patients’ Utilities: Can the Ends Justify the Means?,” Medical Care 27, 269–281. {% Dutch book: discusses extension to multi-valued logic with events that can take more values than true or untrue, following up on work by Jeff Paris. %} Mundici, Daniele (2006) “Bookmaking over Infinite-Valued Events,” International Journal of Approximate Reasoning 43, 223–240. {% foundations of probability %} Munera, Hector A. (1992) “A Deterministic Event Tree Approach to Uncertainty, Randomness and Probability in Individual Chance Processes,” Theory and Decision 32, 21–55. {% %} Munier, Bertrand R. (1988, ed.) “Risk, Decision and Rationality,” 545–556, Reidel, Dordrecht. {% %} Munier, Bertrand R. (1991) “Nobel Laureate, The Many Other Allais Paradoxes,” Journal of Economic Perspectives 5 no. 2, 179–199. {% %} Munier, Bertrand R. (1991) “Market Uncertainty and the Process of Belief Formation,” Journal of Risk and Uncertainty 4, 233–250. {% %} Munier, Bertrand R. (1992) “Expected Utility versus Anticipated Utility - Where Do We Stand,” Fuzzy Sets and Systems 49, 55–64. {% %} Munier, Bertrand R. & Mohammed Abdellaoui (1991) “Expected Utility Violations: An Appropriate and Intercultural Experiment.” In Attila Chikàn et al. (eds.) Progress in Decision, Utility and Risk Theory, Kluwer Academic Publishers. {% %} Munier, Bertrand R. & Mark J. Machina (1994) “Models and Experiments in Risk and Rationality.” Kluwer Academic Publishers, Dordrecht. {% Supervisors were Mokken and Saris. March 1998. Uses generalization of bisymmetry to n dimensions, so what Chew called event commutativity, to characterize the quasilinear mean. Ch. 2 describes an experimental test of the condition in the context of performances of students. %} Münnich, Àkos (1998) “Judgement and Choice.” Ph.D. Dissertation, University of Rotterdam, the Netherlands. {% Uses bisymmetry condition, for more than two states of nature, to get expected utility functional. Is formulated in context of aggregation over persons. %} Münnich, Àkos, Gyula Maksa, & Robert J. Mokken (1999) “Collective Judgement: Combining Individual Value Judgments,” Mathematical Social Sciences 37, 211–233. {% Extends the bisymmetry functional equation to n variables. More advanced results can be found in Nakamura (1990 JET, 1992, 1995) and an unpublished Chew (1989) paper. %} Münnich, Àkos, Gyula Maksa, & Robert J. Mokken (2000) “n-Variable Bisection,” Journal of Mathematical Psychology 44, 569–581. {% Test it not for risk but for multi-attribute. %} Münnich, Àkos, Gyula Maksa, & Robert J. Mokken (2005) “Testing n-Stimuli Bisymmetry,” Journal of Mathematical Psychology 48, 399–408. {% Reference-dependence in otherwise classical model. Cycles are excluded. %} Munro, Alistair & Robert Sugden (2003) “On the Theory of Reference-Dependent Preferences,” Journal of Economic Behavior and Organization 50, 407–428. {% Refer to my Fuzzy Sets and System paper %} Murofushi, Toshiaki & Michio Sugeno (1989) “An Interpretation of Fuzzy Measures and the Choquet Integral as an Integral with respect to a Fuzzy Measure,” Fuzzy Sets and Systems 29, 201–227. {% %} Murofushi, Toshiaki & Michio Sugeno (1993) “Some Quantities Represented by the Choquet Integral,” Fuzzy Sets and Systems 56, 229–235. {% Extend the Schmeidler (1986) functional representation by considering functions of bounded variation. %} Murofushi, Toshiaki, Michio Sugeno, & Motoya Machida (1994) “Non-Monotonic Fuzzy Measures and the Choquet Integral,” Fuzzy Sets and Systems 64, 73–86. {% probability elicitation %} Murphy, Allan H. & Robert L. Winkler (1970) “Scoring Rules in Probability Assessment and Evaluation,” Acta Psychologica 34, 917–924. {% probability elicitation. Seem to mention that the U.S. National Weather Service (NWS) required its meteorologists since 1965 to give probability judgments in addition to their categorical forecasts of precipitation. %} Murphy, Allan H. & Robert L. Winkler (1974) “Subjective Probability Forecasting Experiments in Meteorology: Some Preliminary Results,” Bulletin of the American Meteorological Society 55, 1206–1216. {% probability elicitation %} Murphy, Allan H. & Robert L. Winkler (1977) “Reliability of Subjective Probability Forecasts of Precipitation and Temperature,” Applied Statistics 26, 41–47. {% Small simplification of a point in Vind’s demonstration showing that Gorman's theorem holds under connectedness rather than arcconnectedness. %} Murphy, F.P. (1981) “A Note on Weak Separability,” Review of Economic Studies 48, 671–672. {% %} Murphy, Terence D. (1981) “Medical Knowledge and Statistical Methods in Early Nineteenth Century France,” Medical History 25, 301–319. {% A nice discussion of regret for decisions about prenatal screening for Down syndrome. Many women do not want to do screening so as to avoid regret in case of induced miscarriage, even if by all outcome measures screening is superior. %} Murray, Rosemary & Jean Beattie (2001) “Decisions about Prenatal Screening.” In Elke U. Weber, Jonathan Baron & Graham Loomes (eds.) Conflict and Tradeoffs in Decision Making, 156–174, Cambridge University Press, Cambridge, UK. {% %} Musgrove, Philip (1985) “Why Everything Takes 2.71828 ... Times as Long as Expected,” American Economic Review 75, 250–252. {% conservation of influence: §34: “Alles, was man fühlt und tut, geschieht irgendwie ‘in der Richtung des Lebens,’ und die kleinste Bewewgung aus dieser Richtung hinaus ist schwer oder erschreckend.” My translation into English: “Everything, which one feels and does, happens somehow ‘in the direction of life,’ and the smallest movement away from this direction is hard or terrifying”. %} Musil, Robert (1930) “Der Mann ohne Eigenschaften.” Rohwolt Publisher, Berlin. {% Christiane, Veronika & I %} Mussweiler, Thomas & Birte Englich (2003) “Adapting to the Euro: Evidence from Bias Reduction,” Journal of Economic Psychology 24, 285–292. {% Seems that he introduced rational expectations. %} Muth, John F. (1961) “Rational Expectations and the Theory of Price Movements,” Econometrica 29, 315–335. {% PT, applications, loss aversion: supports prospect theory; i.e., implications of reference dependence and diminishing sensitivity. They let participants exchange money/lotteries in a market setup, when outcomes are losses. Risk averse for gains, risk seeking for losses: beautiful data supporting this. The resulting equilibria suggest risk seeking for losses, in agreement with prospect theory. When reframed as gains (pp. 818-819), the resulting equilibria suggest risk aversion! The latter was done for only one equilibrium with only 9 subjects. real incentives/hypothetical choice: hypothetical questions (called questionnaires) revealed results that nicely agree with real-incentive market behavior. Some more risk aversion for real incentives. losses from prior endowment mechanism. Done. They must hope that participants do not integrate the total amounts. Some results suggest that loss aversion (Conjecture 1, p. 820) and risk-seeking-for-losses (Conjecture 2, p. 820) decrease with experience. The latter nicely suggests that convex utility for losses reflects diminishing sensitivity rather than intrinsic value. I agree much with the interpretations in this paper. The paper is strange in claiming that learning effects (reducing risk seeking for losses) would violate prospect theory, contrary to writings by Kahneman & Tversky (1986) and others that learning and incentives can make choices more rational. random incentive system: p. 806 top of 2nd column uses it. Footnote 3 there states that the Holt (1986) compound-prospect argument can be ignored. %} Myagkov, Mikhail G. & Charles R. Plott (1997) “Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments,” American Economic Review 87, 801–828. {% %} Mycielski, Jan & Stanislaw Swierczkowski (1964) “On the Lebesgue Measurability and the Axiom of Determinateness,” Fundamentà Mathematicae 54, 67–71. {% time preference; Seems that they compare exponential to hyperbolic, do not consider increasing impatience; linear utility; hypothetical questions; data fitting on individual level; 12 subjects, no mention that they had problems fitting the data. %} Myerson, Joel & Leonard Green (1995) “Discounting of Delayed Rewards: Models of Individual Choice,” Journal of the Experimental Analysis of Behavior 64, 263–276. {% %} Myerson, Roger B. (1979) “An Axiomatic Derivation of Subjective Probability, Utility, and Evaluation Functions,” Theory and Decision 11, 339–352. {% %} Myerson, Roger B. (1981) “Utilitarianism, Egalitarianism and the Timing Effect in Social Choice Problems,” Econometrica 49, 883–897. {% K is a set of objects to choose from. V is a set of votes available to voters. Votes are to be taken abstractly. For every v V, (v) is the number of voters who chose v as t heir vote. For every object k K and v V, Sk(v) is the support that v gives to k. The value of object k is vVSk(v)(v), and the object k with the highest value is chosen. So, every k is evaluated through a k-dependent repetitions-approach (Wakker 1986) evaluation. %} Myerson, Roger B. (1995) “Axiomatic Derivation of Scoring Rules without the Ordering Assumption,” Social Choice and Welfare 12, 59–74. {% Big Japanese data set is analyzed for relation between discounting, decreasing impatience, and smoking. Novelty is that sign effect (less discounting for losses than for gains) is incorporated. P. 1444 end of 4th para they report that: “hyperbolic discounting estimated from monetary choice questions exhibits neither a predicted nor a stable correlation with smoking.” They criticize this measure for being noisy. The measure is derived from intertemporal indifferences (derived from choice list) about receiving in 2 days vs. 9 days, 90 vs. 97 days, and three of 1 month vs. 3 month. So none considers immediate payoff and present bias. P. 1448 explains that the authors use hypothetical choice citing three references (footnote 10) that find no differencve. Given hypothetical anyhow, I would have preferred way longer periods because in short term there is little discounting. They take another question, about whether people did homework fast in their youth (§3.2.2) instead as proxy for discounting. This relates positively with smoking. It can, however, be for reasons different than time attitude. For instance, both smoking and postponing homework are protest attitudes against parents. Sign effect in sense of making discounting less for losses can decrease smoking, which is what the authors claim, but also in sense of making discounting for gains stronger can increase smoking I would say. Opening sentence in §2 strangely connects Becker & Murphy (1988) with forward-looking. In Table 4, the probability of rain at which one takes an umbrella is index of risk seeking P. 1453 §3.3 nicely tests time incariance: if time preference changes if both consumption and decision time change, but their difference remains the same. So, whether one can use stopwatch time. They have the longitudinal data for it, and find it violated. %} Myong-Il Kang and Shinsuke Ikeda (2014) “Time Discounting and Smoking Behavior: Evidence from a Panel Survey, Health Economics 23, 1443–1464. {% %} Myung, Jae I. (2003) “Tutorial on Maximum Likelihood Estimation,” Journal of Mathematical Psychology 47, 90–100. {% Theory is about complexity versus parsimony; it considers not only the number of parameters but also the complexity of the formula. %} Myung, Jae I. & Mark A. Pitt (1997) “Applying Occam’s Razor in Modeling Cognition: A Bayesian Approach,” Psychological Bulletin & Review 4, 79–95. {% error theory for risky choice; Does what title says. %} Myung, Jae I., George Karabatsos, & Geoffrey I. Iverson (2005) “A Bayesian Approach to Testing Decision Making Axioms,” Journal of Mathematical Psychology 40, 205–225. {% Seems that they point out problems of single-agent/representative-agent assumption in data fitting. %} Myung, Jae I., Cheongtag Kim, & Mark A. Pitt (2000) “Towards an Explanation of the Power Law Artifact: Insights from Response Surface Analysis,” Memory and Cognition 28, 832–840. {% value of information; rekenen geloof ik gewoon maar wat dingen uit binnen EU. %} Nadiminti, Raja, Tridas Mukhopadhyay, & Charles H. Kriebel (1996) “Risk aversion and the Value of Information,” Decision support systems 16, 241–254. {% %} Nagel, Rosemarie (1995) “Unraveling in Guessing Games: An Experimental Study,” American Economic Review 85, 1313–1326. {% This paper follows up on Heinemann, Nagel, & Ockenfels (2009 RESTUD), HNO henceforth, adding a competitive entry game and doing neuro measurements. The first of the two games, the stage hunt game, is as follows. Imagine the 2-player game where each can choose safe (A) or risky (B), with payoffs, for some parameter 0 < x < 15. A B A xx x0 B 0x 1515 The notation A, B is as used in the paper. It is a coordination game. If both go risky, they gain. There are two pure NE (Nash equilibria), (A,A) and (B,B). The randomized NE is ((15x)/15: A, x/15: B) for both players. Note that it has the counterintuitive property of decreasing probability of choosing the safe x as x increases. It is symmetric but not stable. All NE are symmetric, so conceivable if both players are chosen randomly from one “uniform/symmetric” population, but the randomized is not plausible. The second of the two games, the entry game, is as follows. Imagine the 2-player game where each can choose safe (A) or risky (B), with payoffs, for some parameter 0 < x < 15. A B A xx x15 B 15x 00 It is a competitive game. If both go risky, they lose. It is favorable to do what your opponent does not do. If playing against a random member from a big population, and most players do one thing, then it is best to do the other thing. There are two pure NE (Nash equilibria), (A,B) and (B,A), but none is symmetric so they cannot arise in a symmetric game. The randomized NE is (x/15: A, (15x)/15: B) for both players. It has the intuitive property of increasing probability of choosing the safe x as x increases. It is symmetric and stable. In both games, the authors measure for several values of x whether players prefer A or B, and call the switching value the CE. As with HNO, this is an unconventional CE, and they also measure conventional CEs of lotteries, and by transitivity one can derive matching probabilities of the favorable event, being the opponent’s choice B in the stage hunt game and A in the entry game. In the entry game, a level-2 player always does the opposite of a level-1 player, which in some situations leads to the paradox of less taking the safe option x as x increases. Yet the switching value can still serve as a sort of CE. It does show that the effect of x on behavior is complex and sometimes antimonotonic. Therefore, it is not surprising that in the entry game the authors find more switches of preferences as x increases, what they call more entropy. They put this forward as an argument that the entry game is of a different nature. They use the term threshold strategy if there are no switches. Entry games also require more response time. Download 7.23 Mb. Share with your friends:
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