Working Papers
Belief in Mean Reversion and the Law of Small Numbers (joint with Jawwad Noor) R&R (round 2) TE
This paper was previously circulated as "An Axiomatic Approach to the Law of Small Numbers"
Studies show that people systematically underestimate the likelihood of streaks in a random sequence. In a canonical coin-tossing environment, this paper shows that the evidence can be explained by a belief in mean reversion. Such beliefs are represented as if the bias of the coin is history-dependent and “self-correcting”. In a Bayesian inference setting, a belief in mean reversion ensures that the agent never rules out the true parameter. Several directions for theoretical and empirical investigation of beliefs about randomness are suggested.
Updating under Imprecise Information (joint with Yi-Hsuan Lin) Submitted
This paper models an agent that ranks actions with uncertain payoffs after observing a signal that could have been generated by multiple objective information structures. Under the assumption that the agent's preferences conform to the multiple priors model (Gilboa and Schmeidler (1989)) ), we show that a simple behavioral axiom characterizes a generalization of Bayesian Updating. Our axiom requires that whenever all possible sources of information agree that it is more 'likely' for an action with uncertain payoffs to be better than one with certain payoffs, the agent prefers the former. We also provide axiomatizations for several special cases. Finally, we consider the situation where the informational content of a signal is purely subjective. We characterize the existence of a subjective set of information structures under full Bayesian updating for two extreme cases: (i) No ex-ante state ambiguity, and (ii) No signal ambiguity.
Modeling the Modeler (joint with Evan Piermont) (Supplemental Appendix) Submitted
We study a modeler whose goal is to (partially) identify a subject’s type (preferences) through revealed preference analysis. We propose three normative principles for how the modeler should rank choice experiments: Structural Invariance, Identification Separability, and Information Monotonicity. Our main result shows that these principles characterize preferences consistent with maximizing Expected Identification Value, a functional form that unifies several theories of experimental design. A notable special case occurs when the value of identification depends on beliefs given a potential identification, allowing the modeler to view experiments as lotteries. This risk-analogy yields a tractable and intuitive specification.
Deception under the Veil of Noise (joint with Jawwad Noor) Submitted
We study a dynamic predator–prey game in which a predator can conceal its movement under naturally occurring environmental noise. In the safe state, forest noise is i.i.d., whereas in the dangerous state the predator contributes additional noise as it approaches the prey. The prey updates her beliefs about danger from the realized noise sequence and chooses whether to remain vigilant. We characterize equilibrium patterns of noise generated in the forest and show that a marker for deception is a hot-hand effect, whereby streaks persist with increasing probability
A Cognitive Theory of Ambiguity Attitudes (joint with Norio Takeoka and Jianming Xia)
This paper provides axiomatic foundations for a model in which ambiguity attitudes are endogenously determined through cognitive optimization. The decision maker evaluates acts using alternative non-additive aggregation rules and optimally trades off the benefits of less ambiguity-averse evaluation against cognitive cost. The resulting framework generalizes Choquet expected utility and accounts for preference reversals identified by Machina (2009). The model is characterized by a novel axiom, Comonotonic Convexity, which regulates the evaluation of mixtures by requiring the decision maker to avoid hedging whenever it yields no benefit. We interpret this axiom as reflecting aversion to unnecessary complexity in the evaluation of acts.
Alpha-MaxMin Updating Rules for Ambiguous Information (joint with Yi-Hsuan Lin)
This paper develops two belief-updating rules for ambiguous information structures, which map each state of the world to a distribution over sets of signal realizations. Grounded in first principles, our updating rules are derived through contingent planning reasoning that adheres to dynamic consistency. Two distinct equations characterize the resulting families of rules, depending on how a decision maker conceives the order of states and signals. Each rule is parameterized by a single index capturing pessimism or optimism toward ambiguity, and both allow for the possibility that news may be all good or all bad. The rules diverge, however, in two key dimensions: whether state-independent information structures preserve the prior, and whether mixing two information structures yields an intermediate posterior.
Publications
Mixture-betweenness: Uncertainty and Commitment Journal of Economic Theory, Volume 230, December 2025
This paper supersedes “Mixture-Dependent Preference for Commitment”, which develops a version of Theorem 3.1 for Associative Mixture Spaces. The earlier paper is available here
This paper develops axiomatic models of preference under uncertainty and preference for commitment that satisfy Mixture-Betweenness, a weakening of the Independence axiom originally proposed by Chew (1989) and Dekel (1986). A central contribution of the paper is a general representation theorem that can be applied across a wide range of domains.
Revealed Preference and the Subjective State Space Hypothesis , Journal of Mathematical Economics Volume 82, May 2019, Pages 61-68
Dekel et al. (2001) extends Kreps’ (1979) model for preference over menus of deterministic alternatives to a model for preference over menus of lotteries. They show that a simple set of axioms characterizes a representation that can be interpreted as if the agent is uncertain about her future tastes. This taste uncertainty is summarized by a set of possible future preferences which is referred to as the subjective state space. Their approach is axiomatic; thus, testability requires that the entire preference order be observable. This paper provides corresponding revealed preference analysis assuming that only finitely many choices are observed. For a particular class of data sets, it is shown that the characterizing conditions can be reformulated as nonlinear systems of inequalities for which the existence of solutions can be verified using numerical methods. The analysis covers the case where available data involves only menus of alternatives (and not lotteries). Hence, our results also provide revealed preference characterizations for Kreps (1979).
Similarity-based mistakes in choice, with L. Ülkü, Journal of Mathematical Economics Volume 61, December 2015, Pages 152-156
We characterize the following choice procedure. The decision maker is endowed with two binary relations over alternatives, a preference and a similarity. In every choice problem she includes in her choice set all alternatives which are similar to the best feasible alternative. Hence she can, by mistake, choose an inferior option because it is similar to the best. We characterize this boundedly rational behavior by suitably weakening the rationalizability axiom of Arrow (1959). We also characterize a variation where the decision maker chooses alternatives on the basis of their similarities to attractive yet infeasible options. We show that similarity-based mistakes of either kind lead to cyclical behavior.
Work in Progress
Bayesian Adaptive Choice Experiments (joint with Marshall Drake, Neil Thakral, and Linh Tô)
Package
A Subjective Theory of Mean Reversion (joint with Jawwad Noor)
Revealed Preferences and Singed Weighted Utility
Ambiguous Subjective States (joint with Norio Takeoka)
Other Publications
Implications of the Patient Protection and Affordable Care Act on Insurance Coverage and Rehabilitation Use Among Young Adult Trauma Patients with Cheryl Zogg, John Scott, Lindsey Wolf , Thomas Tsai , Peter Najjar, Olubode Olufajo, Eric Schneider, Elliott Haut, Adil Haider, Joseph Canner, JAMA surgery Volume 151, December 2016
Componentes Principales: Las Dimensiones de la Confianza with Kin Gutierrez Olivares y Max Mergenthaler, Laberintos y Infinitos No 39, Pg 35-41 2015