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Part I was reprinted as Harsanyi, John C. (2004) “Games with Incomplete Information Played by “Bayesian” Players, Parts I, II, III,”
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| Part I was reprinted as Harsanyi, John C. (2004) “Games with Incomplete Information Played by “Bayesian” Players, Parts I, II, III,” Management Science 14, 1804–1817.
{% risky utility u = strength of preference v (or other riskless cardinal utility, often called value): seems to say this, with p. 600 subscribing to Bernoulli’s principle. %} Harsanyi, John C. (1975) “Can the Maximin Principle Serve as a Basis for Morality? A Critique of John Rawls’s Theory,” American Political Science Review 69, 594–606. {% %} Harsanyi, John C. (1977) “Rational Behavior and Bargaining Equilibrium in Games and Social Situations.” Cambridge University Press, Cambridge. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value) %} Harsanyi, John C. (1977) “Morality and the Theory of Rational Behavior,” Social Research 44, 623–656. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value); argues strongly, without nuances, in favor of Bayesianism. P. 225 Footnote 2 argues that Savage’s P4, requiring qualitative ordering of probability, is his weakest axiom and is the main one to be weakened, and puts Anscombe & Aumann (1963) forward as a model that did so. %} Harsanyi, John C. (1978) “Bayesian Decision Theory and Utilitarian Ethics,” American Economic Review, Papers and Proceedings 68, 223–228. {% Comments: see at Kadane & Larkey (1982) paper (game theory can/cannot be seen as decision under uncertainty) %} Harsanyi, John C. (1982) “Subjective Probability and the Theory of Games: Comments on Kadane and Larkey’s Paper,” Management Science 28, 120–125. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value): p. 127 is strong on it: “For, contrary to accepted doctrine, a careful analysis of the vNM axioms will show that the utility functions defined by these axioms have nothing to do with people’s like or dislike for the activity of gambling as such. Rather, they express each person’s willingness (or unwillingness) to take risks as determined by the relative importance he or she assigns to alternative desirable or undesirable outcomes, that is to say, by the strength of his or her desire to end up (or not to end up) with any particular outcome.” (Italics from original.) %} Harsanyi, John C. (1988) “Assessing Other People’s Utilities.” In Bertrand R. Munier (ed.) Risk, Decision and Rationality, 127–138, Reidel, Dordrecht. {% %} Harsanyi, John C. (1991) “Normative Validity and Meaning of von Neumann-Morgenstern Utilities.” In Logic, Methodology and Philosophy of Science IX: Proceedings of the Ninth International Conference of Logic, Methodology, and Philosophy of Science, 442–462, Upsala, Sweden. Reprinted in Kenneth G. Binmore, Alan P. Kirman, & Piero Tani (1993, eds.) Frontiers of Game Theory, 307–319, MIT Press, Cambridge, MA. {% Argues that not actual preferences, but informed preferences, are to be the basis of normative decisions. %} Harsanyi, John C. (1997) “Utilities, Preferences, and Substantive Goods,” Social Choice and Welfare 14, 129–145. {% Harsanyi’s ultimate solution to noncooperative game theory; They seem to argue for the backward induction solution to the game where Kohlberg & Mertens (1986) (and I) think forward induction should apply. %} Harsanyi, John C. & Reinhard Selten (1988) “A General Theory of Equilibrium Selection in Games.” MIT Press, Cambridge, MA. {% The paper opens up with “Economics is witnessing the solid beginnings of a revolution in microeconomic theory.” The abstract’s last sentence: “Closer collaboration between theoretic modeling and experiments is clearly seen to be necessary.” %} Harstad, Ronald M. & Reinhard Selten (2013) “Bounded-Rationality Models: Tasks to Become Intellectually Competitive,” Journal of Economic Literature 51, 496–511. {% dynamic consistency: pointed out to me by Dréze in February 1994; pp. 54-55: criticism on compounding probabilities is, however, that in between more information and other decision options became available. A nice early statement of this point! %} Hart, Albert G. (1942) “Risk, Uncertainty, and the Unprofitability of Compounding Probabilities.” In Oskar Lange, Francis McIntyre, & Theodore O. Yntema (eds.) Studies in Mathematical Economics and Econometrics: In Memory of Henry Schultz, 110–118, The University of Chicago Press, Chicago. Reprinted in American Economic Association (This AEA is to be the editor) (1946) Readings in the Theory of Income Distribution (1946) 547–557, Blakiston, Philadelphia. {% The author proposes two more-risky-than orderings on prospects, one according to the measure introduced by Aumann & Serrano (2008), the other according to the measure introduced by Foster & Hart (2009). Equivalent conditions are given. %} Hart, Sergiu (2011) “Comparing Risks by Acceptance and Rejection,” Journal of Political Economy 119, 617–638. {% inverse-S: assumes it in his analysis, so does not test it. Measured utilities/probability weighting (a parameter for every outcome/probabiliity), I think by best-fitting, on three consecutive weeks, to find that they were not stable over time. %} Hartinger, Armin (1999) “Do Generalized Expected Utility Theories Capture Persisting Properties of Individual Decision Makers?,” Acta Psychologica 102, 21‑42. {% PROMIS is an introspective measurement of quality of life/utility. This paper measures both that and the standard EQ-5D, and finds relations between them, so that PROMIS can be transformed into EQ-5D. N = 2623 subjects, representative adult group in US, were used. %} Hartman, John D. & Benjamin M. Craig (2018) “Comparing and Transforming PROMIS Utility Values to the EQ-5D,” Quality of Life Research 27:725–733. {% Theorem 1 in version of 26Sep2017: Assume CEU with linear utility (Anscombe-Aumann). Then capacity is exact iff preference satisfies convexity condition whenever the mix has only two outcomes. Remember here that outcomes are probability distributions, so that a mix of some five-outcome acts can have only two outcomes. %} Hartmann, Lorenz & T. Florian Kauffeldt (2017) “An Axiomatizion of Exact Capacities,” working paper. {% Characterizes the Einhorn-Hogarth weighting function as minimization of the Kullback Leibler distance when the probability should aggregate a number of probability estimates. %} Hartmann, Stephan (2016) “Prospect Theory and the Wisdom of the Inner Crowd,” working paper. {% Seems that he criticizes Lucas’ use of the representative agent. %} Hartley, James E. (1996) “Retrospectives: The origins of the Representative Agent,” Journal of Economic Perspectives 10, 169–177. {% Relate risk attitudes to individual characteristics. gender differences in risk attitudes: women are more risk averse than men, civil servants more than self-employed; decreasing ARA/increasing RRA: they find that rich are less absolute risk averse than poor. %} Hartog, Joop, Ada Ferrer-i-Carbonell, & Nicole Jonker (2002) “Linking Measured Risk Aversion to Individual Characteristics,” Kyklos 55, 3–26. {% %} Hartman, Stanislaw, Jan Mikusìnski, & Leo F. Boron (1961) “The Theory of Lebesgue Measure and Integration.” Pergamon, Oxford. {% Show that medium prizes in lotteries slow down the decrease over time in agents’ inclination to gamble, because of slower learning. %} Haruvy, Ernan, Ido Erev, & Doron Sonsino (2001) “The Medium Prizes Paradox: Evidence from a Simulated Casino,” Journal of Risk and Uncertainty 22, 251–261. {% Alternative characterization of the translated log-power family %} Harvey, Charles M. (1981) “Conditions on Risk Attitudes for a Single Attribute,” Management Science 27, 190–203. {% present value; standard-sequence invariance: equal tradeoffs comparisons condition (p. 1126) is of this kind. §3, Theorem 3 uses this idea to characterize concavity of utility etc., very similar to how I did it in those days, such as in my 1986 paper “Concave Additively Decomposable Representing Functions and Risk Aversion.” Tradeoffs midvalues above Eq. 4 contains a way to measure endogenous utility midpoints. Kirsten&I: seems to have countably infinitely many time points and infinitely many outcomes. Seems to do the following things: provides an axiomatization for discounted utility. Defines concept like timing neutrality, timing averseness and timing proneness, impatience (different than in Koopmans), temporal inequity aversion, absolute timing preferences, relative timing preferences. The exponential discounting model as well as a “relative value discounting model” is axiomatized. In adition, a few functional forms of the instantaneous utility function are axiomatized. %} Harvey, Charles M. (1986) “Value Functions for Infinite-Period Planning,” Management Science 32, 1123–1139. {% Assumes infinitely many time points as in Koopmans (1960), and risk. Formulates many preference conditions that imply functional equations and, hence, particular properties and forms of discounting and utility. Attitudes toward multiperiod risk (p. 648 etc.), for instance, is the intertemporal analog of multivariate risk aversion. %} Harvey, Charles M. (1988) “Utility Functions for Infinite-Period Planning,” Management Science 34, 645–665. {% Assume EU with strictly increasing (I guess) utility. In Theorem 1, the equivalence of (e) and (f) shows that constant absolute risk aversion for all two-outcome prospects with known probabilities implies linear-exponential (CARA) utility, and constant relative risk aversion for all two-outcome prospects with known probabilities implies log-power (CRRA) utility. The theorem considers all transformations of the addition operation. Under continuity of U, conditions only for fifty-fifty prospects is enough. This undervalued paper contains useful general tools for solving functional equations. %} Harvey, Charles M. (1990) “Structural Prescriptive Models of Risk Attitude,” Management Science 36, 1479–1501. {% %} Harvey, Charles M. (1991) “Models of Tradeoffs in a Hierarchical Structure of Objectives,” Management Science 37, 1030–1042. {% %} Harvey, Charles M. (1992) “A Slow-Discounting Model for Energy Conservation,” Interfaces 22, 47–60. {% dynamic consistency; DC = stationarity: uses term “permanence” for DC (dynamic consistency), and distinguishes it carefully from stationarity; discounting normative. Kirsten&I: seems to do infinitely and uncoutably many time points; countably infinitely many consumptions, discrete and not spread over time. %} Harvey, Charles M. (1994) “The Reasonableness of Non-constant Discounting,” Journal of Public Economics 53, 31–51. {% present value: p. 386; Kirsten&I: seems to do infinitely and uncoutably many time points; countably infinitely many consumptions, discrete and not spread over time. dynamic consistency: absolute timing being constant is same as Koopman’s stationarity; P. 389, DC = stationarity: 2nd paragraph gives nice discussion of difference between stationarity and DC (dynamic consistency) (called permanence there). discounting normative, end says: “We conjecture that many of the normative objections to nonconstant timing preferences are in fact objections to nonpermanent timing preferences.” linear utility for small stakes: p. 392 mentions it to defend its linear utility %} Harvey, Charles M. (1995) “Proportional Discounting of Future Costs and Benefits,” Mathematics of Operations Research 20, 381–399. {% risky utility u = strength of preference v (or other riskless cardinal utility, often called value): argue for the use of strength of preference measurements in health care. %} Harvey, Charles M. & Lars-Peter Østerdal (2010) “Cardinal Scales for Health Evaluation,” Decision Analysis 7, 256–281. {% The authors axiomatize discounted utility where the discount function can be general and need not be constant, for continuous outcome streams over a time interval that can be bounded or unbounded, which is useful to have available. It amounts to a special case of Savage’s subjective expected utility, with the time interval as state space. Techniques of Wakker (1993), who like this paper assumes continuous utility, can be used to get countable additivity (his Proposition 4.4), absolute continuity w.r.t. the Lebesgue measure (every Lebesgue null set of time points should be preferentially null and then Radon-Nikodym; this is an easy solution to the open question that the authors state at the end of the first column of p. 286), and only outcome streams with finitely many discontinuities (take algebra of finite unions of intervals and simple functions there, next extend by truncation continuity). The authors use an alternative route, more directly targeted towards their objective. Note that, as the authors indicate, Kopylov (2010) is the first to have characterized the important special case of constant discounting. The authors use the usual Debreu-Gorman type separability to get general additive decomposability, and then a midpoint axiom to get proportionality (their Condition (E) on p. 287which can also be done by bisymmetry or tradeoff consistency). The only real mathematical difference between general (nonconstant) discounted utility and subjective expected utility is that in the former case the total measure of the time space need not be finite (if impatience does not decrease much), whereas under subjective expected utility it always is finite. This complication is delt with in §6. P.s.: on a personal side, I am happy to see that Harvey, many years after retirement, and after his many solid contributions to intertemporal choice including for instance his valuable and underappreciated Harvey (1990 Management Science), together with his younger co-author who encouraged him, made this work see the light of day. %} Harvey, Charles M. & Lars Peter Østerdal (2012) “Discounting Models for Outcomes over Continuous Time,” Journal of Mathematical Economics 48, 284–294. {% dynamic consistency; They take dynamic consistency differently than I do, say that myopic deciders violate it, but sophisticated don’t???? %} Haslam, Nick & Jonathan Baron (1993) Book Review of: Edward F. McClennen (1990) “Rationality and Dynamic Choice: Foundational Explorations,” Cambridge University Press, Cambridge; Journal of Mathematical Psychology 37, 143–153. {% survey on nonEU; on judgment and decision making. P. 668, problem 9, says that theories with nonlinear utilities and nonlinear event-weighting functions are most popular. The paper discusses a list of questions put forward by researchers, without very much structure or lines otherwise. %} Hastie, Reid (2001) “Problems for Judgment and Decision Making,” Annual Review of Psychology 52, 653–683. {% %} Hastie, Reid & Robin M. Dawes (2001) “Rational Choice in an Uncertain World, the Psychology of Judgment and Decision Making.” Sage Publications, Thousand Oaks, CA. {% The authors argue that the distinction between prior and statistical probability that Knight (1921) made was already the distinction between decisions from description and decisions from experience. So, they impose their modern ideas upon classical writings. %} Hau, Robin, Timothy J. Pleskac, & Ralph Hertwig (2010) “Decisions from Experience and Statistical Probabilities: Why They Trigger Different Choices than A Priori Probabilities,” Journal of Behavioral Decision Making 23, 48–68. {% Show that also with large sampling, experienced probabilities are treated differently than described ones. %} Hau, Robin, Timothy J. Pleskac, Jürgen Kiefer, & Ralph Hertwig (2008) “The Description-Experience Gap in Risky Choice: The Role of Sample Size and Experienced Probabilities,” Journal of Behavioral Decision Making 21, 493–518. {% HYE %} Hauber, A. Brett (2009) “Healthy-Years Equivalent: Wounded but not yet Dead,” Expert Review of Pharmacoeconomics & Outcomes Research 9, 265–269. {% %} Haug, Jorgen & Jacob Sagi (2005) “Endogenous Regime Changes in the Term Structure of Real Interest Rates?,” {% In my papers preference is equated with binary choice. This paper takes the word in a different sense, as another primitive besides choice and then not to be equated with it. What Ramsey (1931) called disposition as interpretation of preference is called hypothetical revealed preference in this paper. %} Hausman, Daniel (2011) “Mistakes about Preferences in the Social Sciences,” Philosophy of the Social Sciences 41, 3–25. {% Philosophical book on the meaning of preference. P. 134 seems to write, nicely on behavioral economics, that descriptive theories have to deviate from normative theories, and that one has to use the empirical deviations from rational models to modify preferences: “methodological longing cannot make the theory of rational choice into an accurate theory of actual choice” Infante, Lecouteux, & Sugden (2016) extensively discuss it. %} Hausman, Daniel M. (2012) “Preference, Value, Choice, and Welfare.” Cambridge University Press, Cambridge, UK. {% real incentives/hypothetical choice: for time preferences: finds annual discount rate of no less than 26.4%. %} Hausman, Jerry A. (1979) “Individual Discount Rates and the Purchase and Utilisation of Energy-Using Durables,” Bell Journal of Economics 10, 33–54. {% %} Hausman, Jerry A. (1985) “The Econometrics of Nonlinear Budget Sets,” Econometrica 53, 1255–1282. {% “embedding”: WTP for cleaning up one lake in an area = WTP for cleaning up all lakes in an area. %} Hausman, Jerry A. (1993) “Contingent Valuation: A Critical Assessment.” North Holland, Amsterdam. {% One of three papers in an issue on contingent evaluation. Argues against contingent vauations, mentioning the many biases. In particular, p. 49 ff. criticizes a study by Carson on Australian cable television. P. 54 is very explicit: “ “no number” is still better than a contingent valuation estimate.” %} Hausman, Jerry (2012) “Contingent Valuation: From Dubious to Hopeless,” Journal of Economic Perspectives 26, 43–56. {% Considers lexicographisch EU. %} Hausner, Melvin (1954) “Multidimensional Utilities.” In Robert M. Thrall, Clyde H. Coombs, & Robert L. Davis (eds.) Decision Processes, 167–180, Wiley, New York. {% Dutch book; ordered vector space; Has Hahn’s embedding theorem, which says that every linearly ordered Abelian group can be represented as a subgrou[p of endowed with the lexicographic ordering, with linearly ordered. %} Hausner, Melvin & James G. Wendel (1952) “Ordered Vector Spaces,” Proceedings of the American Mathematical Society 3, 977–982. {% own little expertise = meaning of life: “Even if there is only one possible unified theory, it is just a set of rules and equations. … However, if we discover a complete theory [of physics], it should in time be understandable by everyone, not just by a few scientists. Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason -- for then we should know the mind of God.” The part following the dots is the closing text of the book. Although by intellectual standards this citation is weak I put this citation under a negative key word and, this kind of writing does help to impress people, increase sales, and increase citation scores. Hawking later wrote: “In the proof stage I nearly cut the last sentence in the book. Had I done so, the sales might have been halved.” %} Hawking, Stephen (1988) “A Brief History of Time.” Bantam Dell Publishing Group, New York. {% Nice survey in beginning of paper. %} Hawkins, Scott A. (1994) “Information Processing Strategies in Riskless Preference Reversals: The Prominence Effect,” Organizational Behavior and Human Decision Processes 59, 1–26. {% questionnaire versus choice utility: do what title says. Claim in intro that Rasch analysis, unlike regressions, delivers utilities that satisfy the utility axioms, but I did not find this explained in the paper (did not search line by line). %} Hawthorne, Graeme, Konstancja Densley, Julie F. Pallant, Duncan Mortimer, & Leonie Segal (2008) “Deriving Utility Scores from the SF-36 Health Instrument Using Rasch Analysis,” Quality of Life Research 17, 1183–1193. {% Uses Anscombe-Aumann two-stage model. Characterizes a regret functional for many-option choice functions. That is, from a set of event-contingent prospects ("acts") B, it chooses the prospect f that minimizes the regret (maxgBu(g(.)) u(f(.))). Here is a functional on event-contingous prospects and u a mixture-linear, continuous, nonconstant, utility function (so EU) and homothetic and nondecreasing. %} Hayashi, Takashi (2008) “Regret Aversion and Opportunity Dependence,” Journal of Economic Theory 139, 242–268. {% dynamic consistency: also analyzes dependence on opportunities. Argues that such dependency is normative in contexts where the opportunities give info about the choice alternatives. Distinguishes opportunity dependence from info dependence. End of § 1.1 argues that dynamic consistency implies (generalized) Bayesian updating; oh well! %} Hayashi, Takashi (2011) “Context Dependence and Consistency in Dynamic Choice under Uncertainty: The Case of Anticipated Regret,” Theory and Decision 70, 399–430. {% A decision under uncertainty model where learning means hearing about states of nature you thought impossible before (unforeseen states), but now learn about. You then expand your state space, keeping the conditional subjective probability on what was known before unchanged. Very similar to independent work by Karni & Viero. Does it in an Anscombe-Aumann (1963) setup. %} Hayashi, Takashi (2012) “Expanding State Space and Extension of Beliefs,” Theory and Decision 73, 591–604. {% Characterize a dynamic version of the smooth model of ambiguity (KMM), using a recursive evaluation. %} Hayashi, Takashi & Jianjun Miao (2011) “Intertemporal Substitution and Recursive Smooth Ambiguity Preferences,” Theoretical Economics 6, 423–475. {% Study multiple prior models. In fact is is 2nd order objective probabilityç but generated in a way so complex that subjuects cannot calculate it (p. 357). P. 356 clearly discusses that in maxmin EU the set of priors can reflect both anbiguity and ambiguity-aversion. RIS: they randomly select TWO choices and implement them for real, giving some income effect. Find that non only the max- and min EU from the priors matter, falsifying the multiple priors model, maxmin EU, maxmax EU, and -maxmin EU. Find that also more than the extremes of the set of priors matter (although mathematically a convex set is entirely characterized by it), falsifying the contraction model. Always, intermediate probabilities in the set of priors, and more of its shape than extremes matters. %} Hayashi, Takashi & Ryoko Wada (2010) “Choice with Imprecise Information: An Experimental Approach,” Theory and Decision 69, 355–373. {% Ambiguity aversion is found for rhesus macaques. %} Hayden, Benjamin Y., Sarah R. Heilbronner, & Michael L. Platt (2010) “Ambiguity Aversion in Rhesus Macaques,” Frontiers in Neuroscience 4, Article 166. {% Experiments with St. Petersburg paradox, and WTP. For 20 subjects done with real payments and BDM (Becker-DeGroot-Marschak), but unclear to me how the high payments, crucial here, were guaranteed. They find much risk aversion, and find the median outcome as a good predictor (so something like second-flip outcome). WTP will contribute to that. The theoretical claims in this paper are sometimes a bit strange. Because the expectation is considered undefined the authors write (p. 6): “It is fallacious therefore to argue that the St. Petersburg paradox has an infinite expected value.” Some below it is erroneously suggested that under expected utility repetitions of the game should be disliked extra, whereas the law of large numbers will give the opposite. %} Hayden, Benjamin Y. & Michael L. Platt (2009) “The Mean, the Median, and the St. Petersburg Paradox,” Judgment and Decision Making 4, 256–272. {% %} Hayek, Friedriech A. (1960) “The Constitution of Liberty,” Routledge and Kegan Paul, London. {% %} Hays, William L. & Robert L. Winkler (1970) “Statistics: Probability, Inference and Decision,” Volumes I and II. Holt, Rinehart and Winston, New York. {% %} Hazen, Gorden B. (1987) “Subjectively Weighted Linear Utility,” Theory and Decision 23, 261–282. {% dynamic consistency: favors abandoning time consistency, so, favors sophisticated choice, discusses forgone-branch independence explicitly and assumes collapse independence implicitly. Criticizes LaValle & Wapman (1986); the paper, however, seems to assume choice only after the resolution of uncertainty, and not before as do LaValle & Wapman. Therefore, it discusses Alias (1) => (a) and (a) => (c). This discussion is useful, pointing out that either resolute choice or sophisticated choice is to be done, and favoring sophisticated choice (not using those terms). The example it gives favoring resolute choice is a different ball game (prior equity in distribution of risks over people). Brings up disadvantage of resolute choice of having to dragg along all past history. %} Hazen, Gorden B. (1987) “Does Rolling Back Decision Trees Really Require the Independence Axiom?,” Management Science 33, 807–809. {% %} Hazen, Gorden B. (1989) “Ambiguity Aversion and Ambiguity Content in Decision Making under Uncertainty,” Annals of Operations Research 19, 415–434. {% utility elicitation %} Hazen, Gorden B., Wallace J. Hopp, James M. Pellisier (1991) “Continuous-Risk Utility Assessment in Medical Decision Making,” Medical Decision Making 11, 294–304. {% %} Hazen, Gorden B. & Jia-Sheng Lee (1991) “Ambiguity Aversion in the Small and in the Large for Weighted Linear Utility,” Journal of Risk and Uncertainty 4, 177–212. {% Nice. %} Hazewinkel, Michiel (1995, ed.) “Encyclopeadia of Mathematics.” Kluwer Academic Publishers, Dordrecht. {% Assume a cardinal value function V, representing strength of preference, available, as in the Dyer-Sarin value-utility models. Capture effects of satiation and habit formation. %} He, Ying, James S. Dyer, & John C. Butler (2013) “On the Axiomatization of the Satiation and Habit Formation Utility Models,” Operations Research 61, 1399–1410. {% Solve/discuss a number of analytical problems in optimizing portfolio choice under PT (they write CPT), giving closed-form solutions. Consider both when reference point is risk-free rate, and when it is different. The paper cites the close Bernard & Ghossoub (2010). P. 318: their small u is what Wakker (2010) denotes U and calls global utility. Beware that their u (they indicate gain-loss by the subscript) is defined on +, and for a loss x < 0, u(x) gives its utility, as it is with Bernard & Ghossoub (2010). P. 318 ff., §3, discussed in detail the case when the optimal solution is to invest infinitely (ill-posedness). Btw, Kothiyal, Spinu, & Peter P. Wakker (2011 JRU) give truncation-preference conditions that directly show when the PT value of a prospect is infinite. P. 318 penultimate para, strangely, claims that an infinite-investment solution must mean wrong incentives, with footnote 9 neutralizing the claim. P. 319: propose a nice new index of loss aversion, being limxU(x)/U(x). P. 322, 2nd column 2nd para: contrary to what the authors suggest, Köbberling & Wakker (2005) do recommend piecewise utility, e.g. linear or exponential, and only argue against it when power utility. K&W also do point out that the problems do not arise if powers for gains and losses are the same. And K&W do not put inconsistencies of loss aversion central between big and small amounts, but between the same amounts when described in different units (10 dollars versus 1000 cents). %} He, Xue Dong & Xun Yu Zhou (2011) “Portfolio Choice under Cumulative Prospect Theory: An Analytical Treatment,” Management Science 57, 315–331. {% Consider RDU with inverse-S shaped probability weighting. They also give roles to aspiration, fear, and hope levels of Lopes. They propose as index of fear the Pratt-Arrow index of w, which they define for general p but apparently only want to use near p = 1. Indexes of hope and aspiration are also proposed. Numerical illustrations and applications to portfolio optimization are given. %} He, Xue Dong & Xun Yu Zhou (2016) “Hope, Fear, and Aspirations,” Mathematical Finance 26, 3–50. {% %} Health Psychology (1995) Vol. 14 no. 1, on HIV {% value of information: sophisticated calculations of it are done in medical decision making. This paper reviews them. %} Heath, Anna, Ioanna Manolopoulou, & Gianluca Baio (2017) “A Review of Methods for Analysis of the Expected Value of Information,” Medical Decision Making, forthcoming. {% Investigate stock option exercise by over 50,000 employees. (Shifting) reference points, different from status quo but based for example on maximal past performance, with risk aversion for gains and risk seeking for losses, could explain things. concave utility for gains, convex utility for losses: the assumption of concave utility for gains and convex utility for losses explains their data well. The location of the reference point is a central point in their analysis. The paper never considers loss aversion. I would expect that for the mixed case, where we are close to the reference point and the option may end above but also below the reference point, we would find extreme risk aversion because of loss aversion. Thus, risk aversion is moderate for very low reference points, extreme for intermediate reference points, and low (even risk seeking) for high reference points. But none of that is reported or discussed. %} Heath, Chip, Steven Huddart, & Mark Lang (1999) “Psychological Factors and Stock Option Exercise,” Quarterly Journal of Economics 114, 601–627. {% %} Heath, Chip, Richard P. Larrick, & George Wu (1999) “Goals as Reference Points,” Cognitive Psychology 38, 79–109. {% ambiguity seeking: football & politics study reveals ambiguity seeking. Download 7.23 Mb. Share with your friends:
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