Working Papers 2020
Working Paper 1-2020
What are axiomatizations good for?
Itzhak Gilboa, Andrew Postlewaite, Larry Samuelson and David Schmeidler
Do axiomatic derivations advance positive economics? If economists are interested in predicting how people behave, without a pretense to change individual decision making, how can they benefit from representation theorems, which are no more than equivalence results? We address these questions. We propose several ways in which representation results can be useful and discuss their implications for axiomatic decision theory.
Published: Theory and Decision, 86 (2019), 339-359.
Working Paper 2-2020
States and Contingencies: How to Understand Savage without Anyone Being Hanged
Itzhak Gilboa, Stefania Minardi, Larry Samuelson and David Schmeidler
Models of decision making under uncertainty gain much of their power from the speci cation of states so as to resolve all uncertainty. However, this speci cation can undermine the presumed observabil- ity of preferences on which axiomatic theories of decision making are based. We introduce the notion of a contingency. Contingencies need not resolve all uncertainty, but preferences over functions from contin- gencies to outcomes are (at least in principle) observable. In suciently simple situations, states and contingencies coincide. In more challenging situations, the analyst must choose between sacri cing observability in order to harness the power of states that resolve all uncertainty, or preserving observability by working with contingencies.
La Revue économique, forthcoming (2019)
Working Paper 3-2020
No-Betting Pareto under Ambiguity
Itzhak Gilboa and Larry Samuelson
It has been argued that Pareto-improving trade is not as compelling under uncertainty as it is under certainty. The former may involve agents with different beliefs, who might wish to execute trades that are no more than betting. In response, the concept of No-Betting Pareto dominance was de ned to capture Pareto improvements that can also be rationalized by common prob- abilities. In this paper we argue that this de nition might be too narrow for use when agents are not Bayesian. Agents who face ambiguity might wish to trade in ways that can be justi ed by common ambiguity, though not necessarily by common probabilities. We accordingly extend the notion of No-Betting Pareto dominance to characterize trades than are "No-Betting Pareto" ranked according to the maxmin expected utility model.
Working Paper 4-2020
What Were You Thinking? Revealed Preference Theory as Coherence Test
Itzhak Gilboa and Larry Samuelson
Theory can be used to test the logic of intuitive decision making|one may ask whether a given set of decisions can be justi ed by a decision theoretic model in a given class. Indeed, in principal-agent settings, such justifications may be required|a manager of an investment fund may be asked what beliefs she had in mind when making nancial decisions for her clients, or when evaluating assets and liabilities. While such a question is formally equivalent to a revealed preference question, our motivation
suggests di erent assumptions about observable data. In this paper we assume that states and utilities are observable, and ask which collections of uncertain-act evaluations can be simultaneously justi ed by a single probability (for a Bayesian agent) and by a single set of probabilities (for a maxmin expected utility agent). We use a linear-programming-based argument to develop characterization results for each case.
Working Paper 5-2020
What Should a Firm Know?Protecting Consumers' Privacy Rents
Daniel Bird and Zvika Neeman
A monopolistic rm observes a signal about the state of the world and then makes a take-it-or-leave-it o er to an uninformed consumer who has recourse to some outside option. We provide a geometric characterization of the rm's information structure that maximizes the consumer's surplus: the optimal regime partitions the space of payo states into polyhedral cones with disjoint interiors. We interpret our results in terms of the maximization of the consumer's \privacy rents." We illustrate and motivate our approach through an example of the regulation of the privacy of genetic information.
Working Paper 6-2020
Theories and Cases in Decisions under Uncertainty
Itzhak Gilboa, Stefania Minardi Larry Samuelson
We present and axiomatize a model that combines and generalizes theory-based and analogy-based reasoning in the context of decision under uncertainty. An agent considers a set of theories describing the data generating process that she observes, and her beliefs over theories are given by decision weights. She also remembers and puts weight on similarity to past cases. When a case is added to her memory and a new problem is encountered, two types of learning take place. First, the decision weight assigned to each theory is multiplied by its conditional probability (given the realized case). Second, subsequent problems are assessed for their similarity to past cases, including the newly-added case. If no weight is put on past cases, the model is equivalent to Bayesian reasoning over the theories. However, when this weight is positive, the learning process continually adjusts the balance between case-based and theory-based reasoning. In particular, a "black swan" which is considered a surprise by all theories would shift the weight to case-based reasoning.
Working Paper 7-2020
Supply-Side Variation in the Use of Emergency Departments
Dan Zeltzer, Liran Einav, Avichai Chasid, Ran D. Balicer
We investigate the role of person-speci c and place-speci c factors in explaining geographic variation in emergency department (ED) utilization using detailed data on 150,000 patients who moved regions within Israel. We observe a sharp change in the probability of an ED visit following a move that is equal to half of the destination- origin difference in the average ED utilization rate. In contrast, we nd no change
in the probability of having an unplanned hospital admission (that is, via the ED), implying that the entire change is driven by ED visits that do not lead to hospital admission. Similar results are obtained in our complementary event-study analysis, which uses hospital entry as a source of variation. The results from both approaches suggest that supply-side variation in ED access a ects only the less severe cases|for which close substitutes likely exist|and that variation across ED physicians in their propensity to admit patients is not explained by place-speci c factors, such as di erences in incentives, capacity, or diagnostic quality.
Working Paper 8-2020
Cheating with (Recursive) Models
Kfir Eliaz, Ran Spiegler and Yair Weiss
To what extent can misspeci ed subjective models distort correlations? We study an \analyst" who utilizes models that take the form of a recursive system of linear regression equations. The analyst ts each equation to an objective empirical distribution. We characterize the maximal pairwise correlation that the analyst's model can predict given a generic objective covariance matrix, subject to the constraint that the estimated model does not distort the mean and variance of individual variables. We show that as the number of variables in the model grows, the estimated pairwise correlation can become arbitrarily large, regardless of the objective correlation.
Working Paper 9-2020
A Simple Model of a Money-Management Market with Rational and Extrapolative Investors
I analyze a simple model of competition in fees among mutual funds. The funds are vertically differentiated in terms of the expected return they can generate for investors. Following Berk and Green (2004), I assume that a fund’s net return is decreasing in the amount of capital it manages, and that there is an infinite supply of capital by rational investors. Unlike the Berk-Green model, I assume there is also a finite supply of capital by non-rational investors who naively chase recent net returns. Investor behavior and the funds’ fee profile induce a long-run average amount of managed capital for each fund. I analyze Nash equilibrium in the game played by the funds, focusing on the implications of fund skill on fees, capital flows and net performance.
Forthcoming in the European Economic Review
Working Paper 10-2020
Kfir Eliaz, Ran Spiegler and Heidi C. Thysen
We study strategic communication when the sender can inuence the receiver's understanding of messages' quilibrium meaning. We focus on a “pure persuasion" setting, in which the informed sender wants the informed receiver to always choose “accept". The sender's strategy maps each state of Nature to a distribution over pairs consisting of: (i) a multi-dimensional message, and (ii) a “dictionary" that credibly discloses the state-dependent distribution of some of the messsage's components. The receiver does not know the sender's strategy by default; he can only interpret message components that are covered by the dictionary he is provided with. We characterize the sender's optimal persuasion strategy and show that full persuasion is possible when the prior on the acceptance state exceeds a threshold that quickly decreases with message dimensionality. We extend our analysis to situations where interpretation of messages is done by a third party with uncertain preferences, and explore alternative notions of “dictionaries".