A Maximum Theorem for Incomplete Preferences

Leandro Gorno and Alessandro Rivello

Journal of Mathematical Economics 106 (2023), 102822.

Abstract: We extend Berge's Maximum Theorem to allow for incomplete preferences. We provide a Maximum Theorem for a fixed preference that can be represented with a finite multi-utility consisting of continuous and strictly quasiconcave functions. We apply this result to study the continuity properties of the set of Walrasian equilibria in exchange economies in which agents have incomplete preferences and the set of Pareto efficient outcomes in strategic games with varying strategy spaces. We also provide a generalization that relaxes the multi-utility assumption and a more abstract theorem that allows for changing preferences. The latter result is based on a new continuity condition on the domains of comparability of a preference that clarifies why incompleteness often leads to failures of the maximum theorem.

Learning from Manipulable Signals

Mehmet Ekmekci, Leandro Gorno, Lucas Maestri, Jian Sun, and Dong Wei

American Economic Review (2022), pp. 3995-4040.

Abstract: We study a dynamic stopping game between a principal and an agent. The agent is privately informed about his type. The principal learns about the agent’s type from a noisy performance measure, which can be manipulated by the agent via a costly and hidden action. We fully characterize the unique Markov equilibrium of this game. We find that terminations/market crashes are often preceded by a spike in manipulation intensity and (expected) performance. Our model also predicts that, due to endogenous signal manipulation, too much transparency can inhibit learning and harm the principal. As the players get arbitrarily patient, the principal elicits no useful information from the observed signal. 

Working paper version with additional material

Competitive Real Options under Private Information

Leandro Gorno and Felipe Iachan

Journal of Economic Theory 185 (2020), 104945.

Abstract: We study a research and development race by extending the standard investment under uncertainty framework. Each firm observes the stochastic evolution of a new product's expected profitability and chooses the optimal time to release it. Firms are imperfectly informed about the state of their opponents, who could move first and capture the market. We characterize a family of priors for which the game admits a stationary equilibrium. In this case, the equilibrium is unique and can be explicitly constructed. Across games with priors in this family, there is a maximal intensity of competition that can be supported, which is a simple function of the environment's parameters. Away from this family, we offer sufficient conditions for convergence of a non-stationary equilibrium. When these hold, the intensity of competition tends to the maximal possible value. Furthermore, we develop methods that can be useful for other applications, including a modified Kolmogorov forward equation for tracking posterior beliefs and an algorithm for computing non-stationary equilibria.

Revealed Preference and Identification

Leandro Gorno

Journal of Economic Theory 183 (2019), pp. 698-739.

Abstract: This paper studies preference identification in a general framework that allows for partial observability of optimal choices: Decision makers select some optimal alternatives, but not necessarily all of them. While partial observability is a methodologically appealing assumption for empirical applications, it makes recovering preferences much harder. The main result provides abstract conditions on classes of preferences and decision problems ensuring identification. The result is applied to several standard settings demonstrating the power of the method.

Subjective Ambiguity and Preference for Flexibility 

Leandro Gorno and Paulo Natenzon

Journal of Economic Behavior & Organization 154 (2018), pp. 24-32.

Abstract: A preference over menus is monotonic when every menu is at least as good as any of its subsets. We show that every utility representation for a monotonic preference is equal to the minmax value of a decision maker whose payoff depends on the option chosen from the menu and on the realization of a subjective state. This representation suggests a decision maker who faces uncertainty about her own future tastes and who exhibits an extreme form of pessimism with respect to this uncertainty. In the case of finitely many alternatives, we provide a characterization of monotonic preferences which relaxes the submodularity axiom of Kreps (1979). We characterize the minimal state space needed for our representation, and we show that the second-period choice behavior of our decision maker differs from the one implied by the costly contemplation model of Ergin (2003).

The Structure of Incomplete Preferences

Leandro Gorno

Economic Theory 66 (2018), pp. 159-185.

Abstract: I study incomplete preferences as a means to represent indecisiveness. A decomposition into maximal domains of comparability is characterized and used to link optimization of incomplete preferences with maximization of local utility functions. Larger maximal domains are shown to correspond to more decisive preferences. The decomposition can be uniquely recovered from choice data under standard assumptions. Applications to different models within decision theory are discussed.

A Strict Expected Multi-Utility Theorem

Leandro Gorno

Journal of Mathematical Economics 71 (2017), pp. 92-95.

Abstract: This paper integrates two key approaches to the representation of incomplete preferences over lotteries. The main result strengthens the conclusion of the expected multi-utility theorem in Dubra, Maccheroni and Ok (2004) by ensuring that all utility indices involved are Aumann utilities (i.e., yield a strictly increasing expectation). The advantages of the method are demonstrated by parametrizing maximal elements and by providing a novel characterization of Aumann utilities.

Additive Representation for Preferences over Menus in Finite Choice Settings

Leandro Gorno

Journal of Mathematical Economics 65 (2016), pp. 41-47.

Abstract: This paper obtains an additive representation for preferences over subsets of a finite set relaxing the two substantive axioms in Kreps (1979) flexibility theorem. The result implies that the lottery structure and assumptions employed by Dekel, Lipman and Rustichini (2001) to identify the subjective state-space do not introduce extraneous restrictions on deterministic choice behavior. This property does not necessarily hold when additional axioms are imposed.