Assistant Professor • Curriculum vitae

Division of the Humanities and Social Sciences

California Institute of Technology

1200 East California Boulevard,

Pasadena, California, 91125

E-mail: luciano@caltech.edu

**Teaching:**

SS201c: Analytical Found. of Social Sciences

SS211c: Advanced Economic Theory

Two lectures on strategic forecasting: [1][2]

**Research interests:**

Microeconomic theory. Economics of risk and uncertainty. Theories of Information.

Strategic forecasting. Bayesian and interactive epistemology.

- Monotone Additive Statistics

with Xiaosheng Mu, Philipp Strack, and Omer Tamuz.

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary, monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries, as well as a characterization of risk-averse preferences over monetary gambles that are invariant to mean-zero background risks.

- Model and Predictive Uncertainty: A Foundation for Smooth Ambiguity Preferences

with Tommaso Denti.

Smooth ambiguity preferences (Klibanoff, Marinacci, and Mukerji, 2005) describe a decision maker who evaluates each act according to a twofold expectation defined by a utility function, an ambiguity index , and a belief over a set of probabilities. We provide an axiomatic foundation for the representation, taking as a primitive a preference over standard Anscombe-Aumann acts. We study a special case where the set of probabilities is a subjective statistical model that is point identified, i.e. the decision maker believes that the true law can be recovered empirically. Our main axiom is a joint weakening of Savage's sure-thing principle and Anscombe-Aumann's mixture independence. In addition, we show that the parameters of the representation can be uniquely recovered from preferences, thereby making operational the separation between ambiguity attitude and perception, an hallmark feature of the smooth ambiguity representation.

Older draft with results on partial identification. - Twofold Conservatism in Choice under Uncertainty

with Federico Echenique and Jamie Vinson.

Conservatism in choice under uncertainty means that a status-quo is abandoned in favor of some alternative only if it is dominated. The standard model of conservative choice introduced by Bewley introduces multiple decision criteria, and calls the status quo dominated when all criteria agree that the alternative is better than the status quo. We consider the case when multiple criteria are used to evaluate the status quo and the alternative, but cannot be used to rank them. The alternative is chosen only if it is preferable to the status quo even when the first is evaluated according to the worst-case scenario, and the second according to the best-case scenario. The resulting model is one of obvious dominance, or twofold conservatism.

- Background Risk and Small-Stakes Risk Aversion

with Xiaosheng Mu, Philipp Strack, and Omer Tamuz.

We show that under plausible levels of background risk, no theory of choice under risk---such as expected utility theory, prospect theory, or rank dependent utility---can simultaneously satisfy the following three economic postulates: (i) Decision makers are risk-averse over small gambles, (ii) they respect stochastic dominance, and (iii) they account for background risk.

- The Cost of Information

with Philipp Strack and Omer Tamuz.

We develop an axiomatic theory of costly information acquisition. Our axioms capture the idea of constant marginal costs in information production: the cost of generating two independent signals is the sum of their costs, and the cost of generating a signal with probability half equals half the cost of generating it deterministically. Together with a monotonicity and a continuity conditions, these axioms completely determine the cost of a signal up to a vector of parameters, one for each pair of states of nature. These parameters have a clear economic interpretation and determine the difficulty of distinguishing between different states. The resulting cost function, which we call log-likelihood ratio cost, is a linear combinations of the Kullback-Leibler divergences (i.e., the expected log-likelihood ratios) between the conditional signal distributions. We argue that this cost function is a versatile modeling tool, and that in various examples of information acquisition it leads to more realistic predictions than the approach based on Shannon entropy.

- Stable Matching under Forward-Induction Reasoning

A standing question in the theory of matching markets is how to define stability under incomplete information. The crucial obstacle is that a notion of stability must include a theory of how beliefs are updated in a blocking pair. This paper proposes a novel epistemic approach. Agents negotiate through offers. Offers are interpreted according to the highest possible degree of rationality that can be ascribed to their proponents, in line with the principle of forward-induction reasoning. This approach leads to a new definition of stability. The main result shows an equivalence between this notion and “incomplete-information stability,” a cooperative solution concept recently put forward by Liu, Mailath, Postlewaite and Samuelson (2014). The result implies that forward-induction reasoning leads to efficient matchings under standard supermodularity conditions.

- From Blackwell Dominance in Large Samples to Rényi Divergences and Back Again

with Xiaosheng Mu, Philipp Strack, and Omer Tamuz, Econometrica, 2021. - Testable Forecasts

Theoretical Economics, 2021. - Aggregate Risk and the Pareto Principle

with Nabil Al-Najjar, Journal of Economic Theory, 2020. - Stochastic Dominance under Independent Noise

with Philipp Strack and Omer Tamuz, Journal of Political Economy, 2020 - An Abstract Law of Large Numbers

with Nabil Al-Najjar, Sankhya, Series A, 2020. - An Axiomatic Theory of Inductive Inference

with Alvaro Sandroni, Philosophy of Science, 2018. - Choice under Aggregate Risk

with Nabil Al-Najjar, Theory and Decision, 2016. - Claim Validation

with Nabil Al-Najjar and Alvaro Sandroni, American Economic Review, 2014. - Merging and Testing Opinions

with Nabil Al-Najjar and Alvaro Sandroni, Annals of Statistics, 2014.