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§3 (p. 296 in English translation) refers to Bertrand (1889) for idea that equally probable judgment can be inferred from equal willingness to bet either way. %}
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de Finetti, Bruno (1931) “Sul Significato Soggettivo della Probabilità,” Fundamenta Mathematicae 17, 298–329. Translated into English by Mara Khale as “On the Subjective Meaning of Probability,” in Paola Monari & Daniela Cocchi (1993, eds.) “Probabilità e Induzione,” 291–321, Clueb, Bologna. {% The necessary and sufficient conditions for EU with a continuous strictly increasing utility U are: [1] CE(x) = x; [2] Strict stochastic dominance; [3] CE(F) = CE(F*) ==> CE(tF+(1-t)G) = CE(tF*+(1-t)G) for all 0 < t < 1. (pp. 379-380). P. 380 explains that this condition is close to associativity as in Nagumo (1930) and Kolmogorov (1930). Condition [3] above is nothing other than the celebrated independence condition. Should we then credit de Finetti as the first to have had the vNM EU characterization? I asked my Italian colleague Enrico Diecidue to read the whole paper to check if anywhere de Finetti points out that the weights are probabilities and that this can concern decision under risk. But he nowhere does. Maybe deliberately because he wanted to push subjective probabilities with his famous statement “Probability does not exist.” Anyway, for this reason I do not credit de Finetti for preceding vNM. Muliere & Parmigiani (1993, p. 423) cite de Finetti (1952, 1964) for discussing the decision interpretation. Nagumo (1930) and Kolmogorov (1930), cited by de Finetti, had such results before, but only for equally likely prospects, which comprises all prospects with rational probabilities, and where their independence condition was the associativity condition for taking means. P. 386 bottom shows the Pratt-Arrow result that CEs (certainty equivalents) are smaller the more concave utility is. %} de Finetti, Bruno (1931) “Sul Concetto di Media,” Giornale dell’Istituto Italiano degli Atturia 2, 369–396. {% utility = representational?: this paper expresses, unfortunately, the viewpoint that the only criterion for rationality is preference coherence. P. 174 of English translation (1989): “… however an individual evaluates the probability of a particular event, no experience can prove him right, or wrong; nor in general, could any conceivable criterion give any objective sense to the distinction one would like to draw, here, between right and wrong.” de Finetti has many such narrow views, showing that he is not of the same intellectual league as the kindred spirits Savage or Ramsey. Dennis Lindley, at age 90, in an interview by Tony O’Hagan in 2013, cited de Finetti on this narrow view and sided with de Finetti, stating “coherence is all.” He also, rightfully, pointed out that de Finetti’s writings are obscure. %} de Finetti, Bruno (1931) “Probabilism,” Logos 14, 163–219. Translated into English by Maria Concetta Di Maio, Maria Carla Galavotti, & Richard C. Jeffrey as: de Finetti, Bruno (1989) “Probabilism,” Erkenntnis 31, 169–223. {% Introduced multivariate risk aversion preceding Richard (1975). %} de Finetti, Bruno (1932) “Sulla Preferibilità,” Giornale degli Economisti e Annali di Economia 11, 685–709. {% Explains that probabilities cannot be modeled as multi-valued logic (degree of truth). The reason is that the degree of belief of a composition of propositions is not determined only by the degree of belief of the separate propositions. See also Dubois & Prade (2001). %} de Finetti, Bruno (1936) “La Logique de la Probabilité.” In Actes du Congres International de Philosophie Scientifique a Paris 1935. Tome IV, 1–9, Hermann et Cie, Paris. {% Dutch book; Footnote (a) in a 1964 translation says that he viewed the reliance of his book argument on money and its game-theory complications as potential short-comings. The original 1937 version apparently did not have these things stated. linear utility for small stakes %} de Finetti, Bruno (1937) “La Prévision: Ses Lois Logiques, ses Sources Subjectives,” Annales de l’Institut Henri Poincaré 7, 1–68. Translated into English by Henry E. Kyburg Jr., “Foresight: Its Logical Laws, its Subjective Sources,” in Henry E. Kyburg Jr. & Howard E. Smokler (1964, eds.) Studies in Subjective Probability, 93–158, Wiley, New York; 2nd edn. 1980, 53–118, Krieger, New York. {% Conjectured that qual.probabilityaxioms suffice to give repr.probabilitymeas. %} de Finetti, Bruno (1949) “La “Logica del Plausible” Secondo la Concezione di Pòlya,” Atti della XLII Riunione della Società Italiana per il Progresso delle Scienze, 227–236. {% foundations of probability %} de Finetti, Bruno (1951) “Recent Suggestions for the Reconciliation of Theories of Probability.” In Jerzy Neyman (ed.) Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley. {% P. 77 following Theorem 3.4.1 on the Pratt-Arrow measure: On p. 700/701, the following paper introduced, before Pratt/Arrow, the Pratt/Arrow measure u''/u' and its elementary properties such as: - it being a measure of concavity; - the 50/50 gamble for gaining or losing h being equivalent to losing h2 divided by the measure (P.s.: that’s the special case of risk premium when expected value is zero); - the measure also being related to an excess probability for gaining; - it entirely comprising all of u that’s relevant. P. 700 points out that expected utility in a mathematical sense is the associative mean and refers back to his and Kolmogorov’s work on associative means of 1931. Had de Finetti written that one interpretation taking only one sentence also in 1931, he would also have been the predecessor of von Neumann & Morgenstern. %} de Finetti, Bruno (1952) “Sulla Preferibilitá,” Giornale degli Economistii e Annali di Economia 11, 685–709. {% %} de Finetti, Bruno (1953) “Role de la Théorie des Jeux dans l’Économie et Role des Probabilités Personnelles dans la Théorie des Jeux” (including discussion). Colloques Internationaux du Centre National de la Recherche Scientifique (Econométrie) 40, 49–63. {% De Finetti independently discovered the idea of proper scoring rules in this paper, not knowing Brier (1950), Good (1952), or McCarthy (1956), for one reason because he did not speak English. This point was confirmed by Savage (1971, 2nd para of 2nd column of p. 783). %} de Finetti, Bruno (1962) “Does It Make Sense to Speak of “Good Probability Appraisers”?”. In Isidore J.Good (ed.) The Scientist Speculates: An Anthology of Partly-Baked Ideas, William Heinemann Ltd., London. Reprinted as Ch. 3 in Bruno de Finetti (1972) “Probability, Induction and Statistics.” Wiley, New York. {% proper scoring rules: seems to propose using proper scoring rules for grading exams. This does not work because for proper scoring rules it is important that there is no other consequence than the payment received from the proper scoring rule. Grades of exams have many more consequences. All the rest of the student’s life society will reward/punish him in unpredictable manners for the grades obtained for the exam. %} De Finetti, Bruno (1965) “Methods for Discriminating Levels of Partial Knowledge Concerning a Test Item,” British Journal of Mathematical and Statistical Psychology 18, 87–123. {% Dutch book; This is a collection of texts, often informal but nice brief expressions, published by de Finetti. Its Ch. 1 is what brought me in the field of decision theory! When I, as a mathematics student in 1978, was amazed about my statistics teacher’s claim, frequentist as I know now, that the probability of life on Mars could not be defined, and was at all treated differently than the probability of a coin toss, he told me that an, in his words, crazy, Italian argued for the same, and wrote the name de Finetti on a piece of paper. With this paper I went to the library, found this book, and read its first chapter. It opened to me the technique of preference foundations, and the possibility to tangibly define something as seemingly intangible as one’s subjective degree of belief. I felt electrified by the idea, and decided that I wanted to work on these ideas. Thanks to the freedom provided by the Dutch academic system and the generous Dutch unemployment benefits of those days, I could work on these ideas even though for some years I could not find other researchers with similar interests, many related references or even journals, and for a while could not find a paid job to do this work. I hope that these ideas can be as magic to the readers as they have always been to me. Preface, pp. xviii – xxiv explain why it is useful notation to equate events with their indicator functions, and probabilities of events with expectations of their indicator functions. %} de Finetti, Bruno (1972) “Probability, Induction and Statistics.” Wiley, New York. {% Book, preface p. x, opens with the famous: “Probability does not exist.” utility = representational?: p. 8 seems to write: “From the theoretical, mathematical point of view, even the fact that the evaluation of probability expresses somebody’s opinion is then irrelevant. It is purely a question of studying it and saying whether it is coherent or not; i.e., whether it is free of, or affected by, intrinsic contradictions. In the same way, in the logic of certainty one ascertains the correctness of the deductions but not the accuracy of the factual data assumed as premisses.” Pp. 22-23 explain that this is meant to be a text book and that, therefore, references are minimized. Dutch book; Ch. 3 is, probably, the best account available in the literature about the book argument. §3.4 ff. discuss the domain on which preference is defined due to book argument, and that it can be a subset of the set of all acts. §5.4 discusses proper scoring rules. §5.5 gives many applications of proper scoring rules, to expert-opinion elicitation such as geologists for oil drilling, forecasting sports events, replies to multiple choice, P. 196, §5.5.7, footnote there, recognizes game-theoretic complications of book argument when opponent is better informed. §4.17: seems to discuss inner products so as to deal with covariance etc. %} de Finetti, Bruno (1974) “Theory of Probability.” Vol. I. Wiley, New York. {% Seems to say that risky utility u = transform of strength of preference v %} de Finetti, Bruno (1979) “A Short Confirmation of My Standpoint.” In Maurice Allais & Ole Hagen (1979, eds.) Expected Utility Hypotheses and the Allais Paradox, 161, Reidel, Dordrecht. {% Seems to argue, from a narrow static Bayesian viewpoint, that higher-order probabilities is just a misunderstanding. %} de Finetti, Bruno (1977) “Probabilities of Probabilities: A Real Problem or a Misunderstanding?” In Ahmed Aykac & Carlo Brumat (eds.) New Directions in the Application of Bayesian Methods, 1–10, North-Holland, Amsterdam. {% Dutch book; proper scoring rules %} de Finetti, Bruno (1981) “Discussion. The Role of 'Dutch Books' and of 'Proper Scoring Rules',” British Journal for the Philosophy of Science 32, 55–56. {% proper scoring rules: gives a table of some data of his probability scoring experiment. It concerns, however, a measurement of 1971 and not of 1961/1962. It also suggests that not much data were collected, and that things were left unfinished. %} de Finetti, Bruno (1982) “Exchangeability in Probability and Statistics.” In George S. Koch & Fabio Spizzichino (eds.) Exchangeability in Probability and Statistics (Proceedings of the International Conference on Exchangeability in Probability and Statistics, Rome, 6th -9th April, 1981, in honour of professor Bruno de Finetti, 1–6, North-Holland, Amsterdam. {% %} de Finetti, Bruno & Leonard J. Savage (1962) “Sul Modo di Scegliere le Probabilità Iniziali,” Sui Fondamenti della Statistica Biblioteca del Metron Series C 1, 81–47 (English summary, pp. 148-151). {% Mooie 60er jaren visies van een socioloog op de welvaartsstaat en tegen de vereconomisering tegenwoordig. %} De Gier, Erik (2001) “De Sociologische Interventie.” {% %} de Giorgi, Enrico & Thorsten Hens (2006) “Making Prospect Theory Fit for Finance,” Financial Markets and Portfolio Management 20, 339–360. {% %} De Giorgi, Enrico, Thorsten Hens, & Janos Mayer (2007) “Computational Aspects of Prospect Theory with Asset Pricing Applications,” Computational Economics 29, 267–281. {% Due to nonconvexity of PT, no equillibria need to exist. Assume finite state space. %} De Giorgi, Enrico, Thorsten Hens, & Marc Oliver Rieger (2010) “Financial Market Equilibria with Cumulative Prospect Theory,” Journal of Mathematical Economics 46, 633–651. {% Surveys the many conditions of strong and weak risk aversion, preference for diversification, 2nd order risk aversion, and the like, giving logical relations both for risk and uncertainty, assuming, EU, or RDU, or no model at all. P. 147 middle: the paper assumes continuity throughout. %} De Giorgi, Enrico G. & Ola Mahmoud (2016) “Diversification Preferences in the Theory of Choice,” Decisions in Economics and Finance 39, 143–174. {% Model with stochastic reference point. If chosen to optimize, endogenously, then coincides with optimal consumption without loss aversion. Hence there will be an exogenous component to loss aversion and reference dependence. The authors develop a model with a sticky reference point, that fits historical IS investment benchmark data well. %} De Giorgi, Enrico G. & Thierry Post (2011) “Loss Aversion with a State-Dependent Reference Point,” Management Science 57, 1094–1110. {% Gives no clear-cut advices but discusses many complications. Argues for instance that it should not matter whether you invest for the short or the long term; etc. %} De Jong, Frank (2003) “Is Mijn Pensioen nog wel Veilig? Over Sparen en Beleggen voor Later.” (Inaugurale rede.) Department of Economics, University of Amsterdam, Amsterdam, the Netherlands. {% Opening page gives many references that people distort probabilities, utilities, and other things in the direction of justifying their preference. Experiment does the usual psychological thing of finding that things depend on other things. %} DeKay, Michael L., Dalia Patiño-Echeverri, & Paul S. Fischbeck (2009) “Distortion of Probability and Outcome Information in Risky Decisions,” Organizational Behavior and Human Decision Processes 109, 79–92. {% Confirm that deviations from EU (certainty and possibility effects) are reduced under repeated decisions and learning. The authors focus on psychological studies and do not cite economic studies on learning. %} DeKay, Michael L., Dan R. Schley, Seth A. Miller, Breann M. Erford, Jonghun Sun, Michael N. Karim, & Mandy B. Lanyon (2016) “The Persistence of Common-Ratio Effects in Multiple-Play Decisions,” Judgment and Decision Making 11, 361–379. {% %} de Koster, Rene, Hans J.M. Peters, Stef H. Tijs, & Peter P. Wakker (1983) “Risk Sensitivity, Independence of Irrelevant Alternatives and Continuity of Bargaining Solutions,” Mathematical Social Sciences 4, 295–300. Link to paper
De Lapparent, Matthieu (2010) “Attitude toward Risk of Time Loss in Travel Activity and Air Route Choices,” Journal of Intelligent Transportation Systems 14, 166–178. {% N = 107; losses from prior endowment mechanism: was not done, but hypothetical choice was used, because for losses real incentives are hard to implement. The authors argue against losses from prior endowment mechanism because of house money effects (p. 119 last para), and I agree with this viewpoint (would add the more general term income effect as objection against losses from prior endowment mechanism). I also think that for losses hypothetical is better. natural sources of ambiguity; ambiguity seeking for losses: they investigate the competence effects not only for gains, but also for losses (the latter is the novelty.) Use temperatures on more and less known places. They control for the belief component in several ways: (1) They take pairs of places that actually have very similar climates, and the same temperature event for both places. (2) source-preference directly tested: they test EXACTLY the source preference condition with source preference if a bet on an event and its complement is preferred. (3) They also asked for direct subjective probability judgments. Find the usual competence effect confirmed for gains, but mostly H0 for losses, with a reflection (source preference AGAINST source with most competence) significantly for one of six cases considered. One explanation that they put forward is that loss choices are noisier (p. 129; confirmed by logit parameter ). Each subject made only one choice for each case (and not many as in choice lists when going for indifferences for instance) and then a representative agent was assumed. reflection at individual level for ambiguity: they have the data for it, but do not report. They also test the two-stage model, assuming representative agent, and taking direct judgments of probability as inputs. So, much of the deviation from additivity and EU can then be comprised in the probability judgment. P. 113 1/3 writes that the two-stage model cannot capture source preference, which is true by the basic spirit of that model, although one (not me) could argue that source preference can be captured in the belief component. There is much collinearity between the elevation and curvature parameter (p. 127). The authors take the curvature parameter at its best level, keep it there, and then let only the elevation parameter vary to test source preference (p. 127). It confirms the other claims, being more elevation for known sources under gains (with parameter values similar to Kilka & Weber (2001), and significantly so for all six cases considered, and no significant effects for losses. P. 126 2nd para: assume that weighting function, and not utility, depends on the source. P. 129: choices for losses are noisier, and take more response time, than for gains. %} de Lara Resende, José G., & George Wu (2010) “Competence Effects for Choices Involving Gains and Losses,” Journal of Risk and Uncertainty 40, 109–132. {% foundations of statistics; discussion done in Amsterdam with Molenaar and Linssen %} de Leeuw, Jan (1984) “Models of Data,” Kwantitatieve Methoden 13, 17–30. {% game theory for nonexpected utility %} De Marcoa, Giuseppe & Maria Romaniello (2015) “Variational Preferences and Equilibria in Games under Ambiguous Belief Correspondences,” International Journal of Approximate Reasoning 60, 8–22. {% Do fMRI for simple choice between sure outcome and gamble, where a simple and neat rephrasing makes people risk averse for gains and risk seeking for losses where only the framing and not the terminal wealth is different, and then measure related brain activities. %} de Martino, Benedetto, Dharshan Kumaran, Ben Seymour, & Raymond J. Dolan (2006) “Frames, Biases, and Rational Decision-Making in the Human Brain,” Science 313, August 4, 684–687. {% Citation taken from goodby speach by Thom Bezembinder. P. 719 of de Graaff’s translation: “de Stoïcijnen [gaven] op de vraag hoe in onze geest de keuze tussen twee willekeurige dingen tot stand komt en wat er de oorzaak van is dat wij uit een groot aantal daalders liever de ene dan de andere nemen, hoewel ze allemaal gelijk zijn als antwoord dat dit geestelijke proces buitengewoon is en niet aan regels gebonden, omdat het door een toevallige, bijkomende impuls of buitenaf in ons komt” %} de Montaigne, Michel (1580) “Essays.” Translation into Dutch by Frank de Graaff (1993); Boom, Amsterdam. {% May argue that discrepancies within risky utility measurements is as big as between risky and riskless utility??? %} de Neufville, Richard de & Philippe Delquié (1988) “A Model of the Influence of Certainty and Probability Effects on the Measurement of Utility.” In Bertrand R. Munier (ed.) Risk, Decision and Rationality, 189–205, Reidel, Dordrecht. {% %} de Palma, André, Mohammed Abdellaoui, Giuseppe Attanasi, Moshe Ben-Akiva, Ido Erev, Helga Fehr-Duda, Dennis Fok, Craig R. Fox, Ralph Hertwig, Nathalie Picard, Peter P. Wakker, Joan L. Walker, & Martin Weber (2014) “Beware of Black Swans,” Marketing Letters 25, 269–280. Link to paper
de Palma, André, Moshe Ben-Akiva, David Brownstone, Charles Holt, Thierry Magnac, Daniel McFadden, Peter Moffatt, Nathalie Picard, Kenneth Train, Peter P. Wakker, & Joan Walker (2007) “Risk, Uncertainty and Discrete Choice Models,” Marketing Letters 19, 269–285. Link to paper
de Palma, André, Nathalie Picard, & Jean-Luc Prigent (2008) “Eliciting Utility for (Non)Expected Utility Preferences Using Invariance Transformations,” {% %} De Paola, Maria & Francesca Gioia (2015) “Who Performs Better under Time Pressure? Results from a Field Experiment,” Journal of Experimental Psychology 53, 37–53. {% NRC Handelsblad is a daily newspaper, with 200,000 copies per day, and is the 4th most sold newspaper in the Netherlands. %} de Raat, Friederike, Erik Hordijk, & Peter P. Wakker (2014) “Laat het Los, Al Die Verzekeringen,” NRC Handelsblads 8 February 2014, E18–E19. Link to paper
de Vroon, Bert (1998, ed.) “Betwijfelde Zekerheden.” Universiteitsdrukkerij, Enschede. {% %} De Waegenaere, Anja, Robert Kast, & André Lapied (2003) “Choquet pricing and Equilibrium,” Insurance: Mathematics and Economics 32, 359–370. {% time preference %} De Waegenaere, Anja & Peter P. Wakker (2001) “Nonmonotonic Choquet Integrals,” Journal of Mathematical Economics 36, 45–60. Link to paper Link to comments (Link does not work for some computers. Then can:
de Wit, Johan (1671) “Waardije van Lyf-Renten naer Proportie van Los-Renten” (“The Worth of Life Annuities Compared to Redemption Bonds”). {% Find that status quo effect becomes stronger for larger choice sets. This means that also for a fixed status quo, WARP is violated. %} Dean, Mark , Özgür Kıbrıs, & Yusufcan Masatlioglu (2017) “Limited Attention and Status Quo Bias,” Journal of Economic Theory 169, 93–127. {% DOI: 10.3982/TE1960 biseparable utility: satisfied. event/utility driven ambiguity model: event-driven Assume AA (Anscombe-Aumann) framework with the restrictive backward induction assumption of CE substitution, but do not assume EU for the second-stage lotteries, but Quiggin’s RDU. This is desirable for empirical purposes. P. 380 footnote 7 mentions that omitting the two-stage could be desirable. The authors use an endogenous utility midpoint operation (p. 381), the one used by Ghirardato, Maccheroni, Marinacci, & Siniscalchi (ECMA 2003), which involves some certainty equivalents, and use it to mix acts statewise. On p. 383 they adapt it to decision under risk and mix lotteries by taking as joint distribution of two lotteries the comonotonic distribution (maximizing correlation). Then under RDU and also under biseparable utility the utility midpoints come as under EU. As a youth memory, Wakker (1990 JET) showed that such comonotonic mixtures are preferred less than noncomonotonic ones if and only if pessimism holds under RDU. Fortunately, the authors use only this midpoint operation and not the extended subjective mixture operation as Ghirardato et al. (2003) did. The latter has the problem that it is too far from direct observability, requiring infinitely many observations for its very definition, e.g. for 1/3-2/3 mixtures. An alternative concept of endogenous utility midpoints was used by Baillon, Driesen, & Wakker (2012): if xp ~ yp and xp ~ yp, comonotonic, then is the endogenous utility midpoint between and . This requires fewer indifferences by not using certainty equivalents, and no multistage. Baillon et. al. in their footnote 2 cite several preceding alternative definitions of endogenous utility midpoints. Using the endogenous midpoint operation, the authors define quasi-convexity of preference (Axiom 5 p. 384) and the analog of certainty independence (Axiom 6 p. 386). Thus they get a multiple priors representation for uncertainty. It is reminiscent of Alon & Schmeidler (2014). Importantly, they do not need the EU assumption of the AA framework in this, using the endogenous operation instead. It gives them the freedom to use alternative models for risk, where they characterize a risky analog of multiple priors taking a minimum over RDU functionals. Their characterizing Axiom 4 is bisymmetry-type to get biseparable. They can thus define ambiguity attitudes in more realistic manners, using conditions that, in my terminology, are of the source-preference type. A restriction is in Definition 7 that they only do it for decision makers with the same risk attitudes, as common with the Yaari CE type conditions as used here. P. 386: “The RDU model is arguably the most well known non-expected utility model for objective lotteries. The cumulative prospect theory model of Tversky and Kahneman (1992), for example, is based on this framework.” The authors very properly point out (p. 393 Footnote 31) that ambiguity neutrality means probabilistic sophistication but with added that this involves agreement with objective probabilities. Probabilistic sophistication in itself does not mean much if we do not specify the domain on which it is valid. This paper does it properly. P. 396 points out that they have nontrivial overlap with the cautious model. Their whole analysis is focused on pessimism and aversion, and does not consider insensitivity for instance, which is another direction of generalization that I hope for. Their model is called multiple priors-multiple weighting. %} Dean, Mark & Pietro Ortoleva (2017) “Allais, Ellsberg, and Preferences for Hedging,” Theoretical Economics 12, 377–424. {% correlation risk & ambiguity attitude: seem to find positive correlation between doing Allais and Ellsberg paradox %} Dean, Mark & Pietro Ortoleva (2017) “Is It All Connected? A Testing Ground for Unied Theories of Behavioral Economics Phenomena,” working paper, Columbia University. {% %} Dean, Moira, & Richard Shepherd (2007) “Effects of Information from Sources in Conflict and in Consensus on Perceptions of Genetically Modified Food,” Food Quality and Preference 18, 460–469. {% P. 190 argues that there is more to risk attitude than can be captured in marginal utility. %} Deber, Raisa B. & Vivek Goel (1990) “Using Explicit Decision Rules to Manage Issues of Justice, Risk, and Ethics in Decision Analysis: When It It not Rational to Maximize Expected Utility?,” Medical Decision Making 10, 181–194. {% conservation of influence Patients want physicians to structure the problem and provide probabilities (those two steps are described as “problem solving (PS)” in the paper), but want to influence utilities and decisions; argue that previous studies did not sufficiently distinguish PS from rest. %} Deber, Raisa B., Nancy Kraetschmer, & Jane Irvine (1996) “What Role Do Patients Wish to Play in Treatment Decision Making?,” Arch. Intern. Med. 156, 1414–1420. {% §4 cites von Neumann (1928) for the existence of mixed Nash-equilibrium in noncooperative game theory if preferences are quasi-concave w.r.t. probabilistic mixing. %} Debreu, Gérard (1952) “A Social Equilibrium Existence Theorem,” Proceedings of the National Academy of Sciences 38, 886–893. Reprinted in Gérard Debreu (1983) “Mathematical Economics: Twenty Papers of Gérard Debreu,” Ch. 2, Cambridge University Press, Cambridge. {% Introduced modeling of uncertainty as multiattribute utility %} Debreu, Gérard (1953) “Une Economie de l’Incertain,” Electricité de France. Translated into English as “Economics of Uncertainty” in Gérard Debreu (1983) Mathematical Economics: Twenty Papers of Gérard Debreu, 115–119, Cambridge University Press, Cambridge. {% one-dimensional utility %} Debreu, Gérard (1954) “Representation of a Preference Ordering by a Numerical Function.” In Robert M. Thrall, Clyde H. Coombs, & Robert L. Davis (eds.) Decision Processes, 159–165, Wiley, New York. {% strength-of-preference representation: Theorem on p. 441; Introduced a solvability-like condition: if P(A,B) > z > P(A,D) then there exists C such that P(A,C) = z. %} Debreu, Gérard (1958) “Stochastic Choice and Cardinal Utility,” Econometrica 26, 440–444. {% %} Debreu, Gérard (1959) “Cardinal Utility for Even-Chance Mixtures of Pairs of Sure-Prospects,” Review of Economic Studies 26, 174–177. {% Preface, p. viii: “Outstanding among these influences has been the work ... which freed mathematical economics from its traditions of differential calculus and compromises with logic.” Seems to be among the first to use the state-preference approach where states of nature are like dimensions of commodity bundles, like Arrow (1953). %} Debreu, Gérard (1959) “Theory of Value. An Axiomatic Analysis of Economic Equilibrium.” Wiley, New York. {% Theorem 2 gives utility-difference representation, using Shapley’s crossover property, assumes existence of quantitative ordinal representation already, and uses solvability; formulates it for choice probabilities I never understood the last lines of Debreu’s proof regarding the function g, and conjecture that he assumes that local additivity implies global additivity on subsets of Cartesian products which need not be true in general. I visited Debreu end 1990s and asked him but he did not remember. I also corresponded with Fishburn who in his 1970 book has similar problems. (See my annotations to his book.) He did not remember either. These things made me work on Chateauneuf & Wakker (1993 JME). %} Debreu, Gérard (1960) “Topological Methods in Cardinal Utility Theory.” In Kenneth J. Arrow, Samuel Karlin, & Patrick Suppes (1960, eds.) Mathematical Methods in the Social Sciences, 16–26, Stanford University Press, Stanford, CA. {% %} Debreu, Gérard (1960), Review of Luce, R. Duncan (1958) “Individual Choice Behavior: A Theoretical Analysis,” American Economic Review 50, 186–188. {% one-dimensional utility; Good reference for existence of continuous representation of preference. %} Debreu, Gérard (1964) “Continuity Properties of Paretian Utility,” International Economic Review 5, 285–293. {% Seems to do the following (I did not read myself): risky utility u = transform of strength of preference v: considers vNM utility u on commodity bundles. Writes u = fov with v least concave utility function, proposes v as riskless utility function and f as reflecting risk attitude. %} Debreu, Gérard (1976) “Least Concave Utility Functions,” Journal of Mathematical Economics 3, 121–129. {% %} Debreu, Gérard & Tjalling C. Koopmans (1982) “Additively Decomposed Quasiconvex Functions,” Mathematical Programming 24, 1–38. {% %} Debreu, Gérard (1983) “Mathematical Economics: Twenty Papers of Gérard Debreu.” Cambridge University Press, Cambridge. {% P. 4, last paragraph: about integrability problem, that it can be bypassed altogether by moving from commodity space to pairs of points. %} Debreu, Gérard (1991) “The Mathematization of Economic Theory,” American Economic Review 81, 1–7. {% Want to refer to my Fuzzy Sets and Systems paper but instead refer to my book %} Decampos, Luis M. & Manuel J. BolaÑos (1992) “Characterization and Comparison of Sugeno and Choquet Integrals,” Fuzzy Sets and Systems 52, 61–67. {% crowding-out: meta-analysis of 128 experiments on crowding-out %} Deci, Edward L., Richard Koestner, & Richard M. Ryan (1999) “A Meta-Analytic Review of Experiments Examining the Effects of Extrinsic Rewards on Intrinsic Motivation,” Psychological Bulletin 125, 627–668. {% Test prudence and temperance. Find some support for prudence, but none for temperance. Results rule out CARA (constant absolute risk aversion) and CRRA utility (under EU). Results agree well with prospect theory (pp. 1414-1415). %} Deck, Cary & Harris Schlesinger (2010) “Exploring Higher Order Risk Effects,” Review of Economic Studies 77, 1403–1420. {% They experimentally extend previous work to risk seeking and risk aversion orders exceeding order 4, and find two prevailing patterns: risk averters are “mixed risk averse”: they dislike an increase in risk for every degree n. Risk lovers are “mixed risk loving”: they like risk increases of even degrees, but dislike increases of odd degrees. %} Deck, Cary & Harris Schlesinger (2014) “Consistency of Higher Order Risk Preferences,” Econometrica 82, 1913–1943). {% %} DeGroot, Morris H. (1970) “Optimal Statistical Decisions.” McGraw-Hill, New York. {% %} DeGroot, Morris H. (1986) “Probability and Statistics.” Addison-Wesley, Reading MA; 2nd edn. {% Discussion of artificial intelligence %} DeGroot, Morris H. (1987) Statistical Science 2, no. 1. {% About brain activities regarding numerical perception. Funny that the first author in this multi-author paper writes “I proposed … ” %} Dehaene, Stanislas, Nicolas Molko, Laurent Cohen, & Anna J. Wilson (2004) “Arithmetic and the Brain,” Current Opinion in Neurobiology 14, 218–224. {% Study risky choices where the outcome received is certain but the time of receipt is risky, citing Chesson & Viscusi (2003) and Onay & Öncüler (2007) as predecessors. Unlike their predecessors, they use real incentives. They find that the Epstein & Zin (1989) model fits better than probability weighting. I think that this is due to the stimuli they chose. The problem of E&Z, as of every outcome-utility driven model, is that they can’t capture the fourfold pattern and, in general, dependence on probability/likelihood. The authors always only compare a 50-50 probability distribution with a mean-preserving spread leading to a 25-75 distribution, so, do not capture dependence on probability. They do have various outcomes: $10, $15, $20 combined with time points 1, 2, 3, 4, 5, 11, 12 weeks, so that outcome-oriented models can capture more variance. %} Dejarnette, Patrick, David Dillenberger, David Gottlieb, & Pietro Ortoleva (2015) “Time Lotteries,” working paper. {% %} Dekel, Eddie (1986) “An Axiomatic Characterization of Preferences under Uncertainty: Weakening the Independence Axiom,” Journal of Economic Theory 40, 304–318. {% For general nonEU, preference for diversification (~ convexity w.r.t. outcome mixing) implies strong risk aversion (called risk aversion in this paper) under continuity, but not the other way around. In the presence of the not-necessary quasi-concavity w.r.t. probabilistic mixing, the two are equivalent. %} Dekel, Eddie (1989) “Asset Demands without the Independence Axiom,” Econometrica 57, 163–169. {% %} Dekel, Eddie (1992) “Discussion of “Foundations of Game Theory” and “Refinements of Nash Equilibrium” .” In Jean-Jacques Laffont (ed.) Advances in Economic Theory I, 76–88, Cambridge University Press, Cambridge. {% %} Dekel, Eddie & Faruk Gul (1997) “Rationality and Knowledge in Game Theory.” In David M. Kreps & Kenneth F. Wallis (1997, eds.), Advances in Economics and Econometrics: Theory and Applications, Vol. 1, Ch. 5, 87–172, Cambridge University Press, Cambridge. {% Epistemic: uses knowledge operator. %} Dekel, Eddie, Barton L. Lipman, & Aldo Rustichini (1998) “Standard State-Space Models Preclude Unawareness,” Econometrica 66, 159–173. {% small worlds; A useful survey on unforeseen contingencies. §1 is on epistemic. §§2-3 can be read independently and give nice summary of decision models on the topic. P. 528 makes a distinction between the state space of the agent and the, more refined, state space of the analyst. This would be a nice basis for Tversky’s support theory. Download 7.23 Mb. Share with your friends:
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