RC_JM_Picture

Roberto Corrao

Job Market Candidate

Research Fields

Economic Theory, Organizational Economics

Job Market Papers

Mediation Markets: The Case of Soft Information (Job Market Paper 1)

Abstract: This paper proposes a theoretical framework that combines information design and mechanism design to analyze markets for mediation services between an informed and an uninformed party. The mediator receives compensation from the informed party and must rely on information that is voluntarily reported. We describe all the outcomes that can be induced via a mediation contract, and compare the optimal outcomes when the mediator has the bargaining power (i.e., monopolistic mediation) with those when the informed party has it. The main finding is that mediation contracts often reveal more information with a monopolistic mediator because they give up some information rents to retain incentive compatibility. Unlike the conventional logic of quality under-provision for physical goods, here the attempt to capture information rents can lead to increased information disclosure. These findings shed light on the controversial matter of whether a monopolistic market for information intermediaries, such as rating agencies for financial securities, is more or less desirable than a competitive one.

The Bounds of Mediated Communication (with Y. Dai, Job Market Paper 2)

Extended abstract in ACM EC Conference Proceedings 2023

Abstract: We study the bounds of mediated communication in sender-receiver games in which the sender's payoff is state-independent. We show that the feasible distributions over the receiver's beliefs under mediation are those that induce zero correlation, but not necessarily independence, between the sender's payoff and the receiver's belief. Mediation attains the upper bound on the sender's value, i.e., the Bayesian persuasion value, if and only if this value is attainable under unmediated communication, i.e., cheap talk. The lower bound is given by the cheap talk payoff. We provide a geometric characterization of when mediation strictly improves on this using the quasiconcave and quasiconvex envelopes of the sender’s value function. In canonical environments, mediation is strictly valuable when the sender has countervailing incentives in the space of the receiver's belief. We apply our results to asymmetric-information settings such as bilateral trade and lobbying and explicitly construct mediation policies that increase the surplus of the informed and uninformed parties with respect to unmediated communication.


Publications

1. Dynamic Opinion Aggregation: Long-run Stability and Disagreement (with S. Cerreia-Vioglio and G. Lanzani)

Forthcoming at The Review of Economic Studies

Abstract: This paper proposes a model of non-Bayesian social learning in networks that accounts for heuristics and biases in opinion aggregation. The updating rules are represented by nonlinear opinion aggregators from which we extract two extreme networks capturing strong and weak links. We provide graph-theoretic conditions on these networks that characterize opinions' convergence, consensus formation, and efficient or biased information aggregation. Under these updating rules, agents may ignore some of their neighbors' opinions, reducing the number of effective connections and inducing long-run disagreement for finite populations. For the wisdom of the crowd in large populations, we highlight a trade-off between how connected the society is and the nonlinearity of the opinion aggregator. Our framework bridges several models and phenomena in the non-Bayesian social learning literature, thereby providing a unifying approach to the field.

2. On Concave Functions over Lotteries (with D. Fudenberg and D. Levine)

Forthcoming at Journal of Mathematical Economics

Abstract: In this note, we disprove the claim that a continuous and concave function over lotteries that also satisfies best-outcome independence admits a representation as a minimum of affine functions by exhibiting a finite-dimensional example. We then show that continuity and upper semi-continuity are equivalent to an "infimum" representation and that this representation is equivalent to continuity and concavity in the finite-dimensional case. Our counterexample has important implications for the theory of convex preferences over lotteries.

3. Nonlinear Pricing with Under-Utilization: A Theory of Multi-Part Tariffs (with J. Flynn and K. Sastry)

American Economic Review, 113, 836-860, 2023

Abstract: We study the nonlinear pricing of goods whose usage generates revenue for the seller and of which buyers can freely dispose. The optimal price schedule is a multi-part tariff, featuring tiers within which buyers pay a marginal price of zero. We apply our model to digital goods, for which advertising, data generation, and network effects make usage valuable, but monitoring legitimate usage is infeasible. Our results rationalize common pricing schemes including free products, free trials, and unlimited subscriptions. The possibility of free disposal harms producer and consumer welfare and makes both less sensitive to changes in usage-based revenue and demand.

4. Epistemic game theory without types structures: An application to psychological games (with P. Battigalli and F. Sanna)

Games and Economic Behavior, 120, 28-57, 2020

Abstract: We consider multi-stage games with incomplete information, and we analyze strategic reasoning by means of epistemic events within a “total” state space made of all the profiles of behaviors (paths of play) and possibly incoherent infinite hierarchies of conditional beliefs. Thus, we do not rely on types structures, or similar epistemic models. Subjective rationality is defined by the conjunction of coherence of belief hierarchies, rational planning, and consistency between plan and on-path behavior. Since consistent hierarchies uniquely induce beliefs about behavior and belief hierarchies of others, we can define rationality and common strong belief in rationality, and analyze their behavioral and lower order beliefs implications, which are characterized by strong rationalizability. Our approach allows to extend known techniques to the epistemic analysis of psychological games where the utilities of outcomes depend on beliefs of order k or lower. This covers almost all applications of psychological game theory.

5. Incorporating belief-dependent motivation in games (with P. Battigalli and M. Dufwenberg)

Journal of Economic Behavior & Organization, 167, 185-218, 2019

Abstract: Psychological game theory (PGT), introduced by Geanakoplos et al. (1989) and significantly generalized by Battigalli and Dufwenberg (2009), extends the standard game theoretic framework by letting players’ utility at endnodes depend on their interactive beliefs. While it is understood that a host of applications that model and/or test the role of emotional and other psychological forces find their home in PGT, the framework is abstract and comprises complex mathematical objects, such as players’ infinite hierarchies of beliefs. Thus, PGT provides little guidance on how to model specific belief-dependent motivations and use them in game theoretic analysis. This paper takes steps to fill this gap. Some aspects are simplified – e.g., which beliefs matter – but others are refined and brought closer to applications by providing more structure. We start with belief-dependent motivations and show how to embed them in game forms to obtain psychological games. We emphasize the role of time and of the perception of players’ intentions. We take advantage of progress made on the foundations of game theory to expand and improve on PGT solution concepts.


Working Papers

1. Optimally Coarse Contracts (with J. Flynn and K. Sastry)

Accepted for presentation at SITE 2023 (Market Design Session)

Abstract: We study a principal-agent model in which actions are imperfectly contractible and the principal chooses the extent of contractibility at a cost. If contractibility costs satisfy a monotonicity property---which is implied by costs that come from difficulties in distinguishing actions when writing the contract---then optimal contracts are necessarily coarse: they specify finitely many actions out of a continuum of possibilities. This result holds even if contractibility costs are arbitrarily small. Applying our results to a nonlinear pricing model, we study how changes in consumer demand, production costs, and informational asymmetries affect the optimally coarse set of quality options.

2. Persuasion and Matching: Optimal Productive Transport (with A. Kolotilin and A. Wolitzky)

Revise and Resubmit at The Journal of Political Economy

Abstract: We consider a general problem of assigning one-dimensional inputs to productive units, which we call optimal productive transport. The model covers Bayesian persuasion (assigning states of the world to posterior beliefs), club economies (assigning workers to firms, or students to schools), robust option pricing (assigning future asset prices to price distributions), and partisan gerrymandering (assigning voters to districts). We show that it is always optimal to pool at most two input types in each unit, and that such pairwise production plans are the only solutions under a non-singularity condition (the twist condition). Our core results provide conditions under which more extreme input pairs should produce higher or lower output, so that output is single-dipped or single-peaked on each set of nested input pairs. We also provide conditions for the optimality of either input segregation or negative assortative matching, where all input pairs are nested. Methodologically, our results rely on novel duality and complementary slackness theorems.

3. (Un-)Common Preferences, Ambiguity, and Coordination (with S. Cerreia-Vioglio and G. Lanzani)

Accepted for presentation at DTEA 22, BSE Summer Forum on Preferences and Bounded Rationality 22, and BSE Summer Forum on Networks 23

Abstract: We study the "common prior" assumption when agents have differential information and preferences beyond subjective expected utility (SEU). We consider interim preferences consistent with respect to the same ex-ante evaluation and characterize them. Notably, agents are mutually dynamic consistent with respect to the same ex-ante evaluation if and only if all the limits of higher-order expectations coincide. Within this framework, we characterize the properties of equilibrium prices in financial beauty contests. Unlike the SEU case, the limit price does not coincide with the common ex-ante expectation. Moreover, high-coordination motives create a divergence between the market price and the fundamental value.

 

4. Nonlinear Fixed Points and Stationarity: Economic Applications (with S. Cerreia-Vioglio and G. Lanzani)

Accepted for presentation at DTEA 22 and ESSET 23

AbstractWe consider the fixed points of nonlinear operators that naturally arise in games and general equilibrium models with endogenous networks, dynamic stochastic games, and in models of opinion dynamics with stubborn agents. We study limit cases that correspond to high coordination motives, infinite patience, and vanishing stubbornness in the applications above. Under monotonicity and continuity assumptions, we provide explicit expressions for the limit fixed points. We show that, under differentiability, the limit fixed point is linear in the initial conditions and characterized by the Jacobian of the operator at any constant vector with an explicit and linear rate of convergence. Without differentiability, but under additional concavity properties, the multiplicity of Jacobians is resolved by a representation of the limit fixed point as a maxmin functional evaluated at the initial conditions. In our applications, we use these results to characterize the limit equilibrium actions, prices, and endogenous networks, show the existence of the asymptotic value in a class of zero-sum stochastic games with a continuum of actions, and compute a nonlinear version of the eigenvector centrality of agents in networks.

5. Targeting in Networks and Markets: An Information Design Approach

Accepted for presentation at NAWES 21

Abstract: In many economic settings, heterogeneous information is aggregated through channels such as social networks or markets' prices. Moreover, information is often controlled and manipulated as to influence the final outcome. The goal of this paper is to introduce aggregation mechanisms in an otherwise standard information design environment and analyze their effect on the information released and on economic outcomes. First, the analysis provides a benchmark irrelevance result: when the designer can target every receiver and the aggregator is linear, it is without loss of optimality to consider public experiments that do not depend on the aggregation mechanism. Differently, if the designer can target only a subset of receivers, then the most prominent individuals are chosen. Next, comparative statics results that link the informativeness of the optimal policy to the underlying aggregation process are discussed. Finally, motivated by robustness concerns, it is shown that the main findings extend to a class of nonlinear aggregation mechanisms.

6. Risk, surprise, randomization, and adversarial forecasters (with D. Fudenberg and D. Levine)

Presented at the plenary "Sir John Hicks Lecture'' by Drew Fudenberg (SAET 2023)

Abstract: An adversarial forecaster representation sums an expected utility function and a measure of surprise that depends on an adversary's forecast.  These representations are concave and satisfy a smoothness condition, and any concave preference relation that satisfies the smoothness condition has an adversarial forecaster representation. Because of concavity, the agent typically prefers to randomize. We characterize the support size of optimally chosen lotteries, and how it depends on preference for surprise.


Work in Progress

1. Common priors, Duality, and No-Trade (with S. Morris, Extended Slides)

Abstract: In this paper, we extend the belief-based approach for the representation of information (cf. Kamenica and Gentzkow, 2011) to a multiple-agent setting. First, we characterize the feasible distributions over higher-order beliefs that can arise from private signals, when the agents share a common prior, in terms of no-trade properties. This allows us to derive interpretable implications of the common prior assumption and to improve on existing results such as the Critical Path Theorem of Kajii and Morris (1997). Second, motivated by the recent growing interest in information design and information robustness, we extend our no-trade characterization to the feasible distributions of coarsenings of higher-order beliefs, such as expectations or actions. Toward this result, we introduce the notion of coarsened type spaces that extend the classical notion due to Harsanyi by allowing each type to be assigned to multiple beliefs that are consistent with given restrictions, such as obedience for action recommendations. With this, we provide a unifying analysis of the common-prior implications as well as a linear-duality toolkit to analyze general information-design problems. From the technical side, we use methods based on the Kantorovich duality of optimal transport and the marginal problem of Strassen (1965) that may reveal fruitful for related applications in information economics.

 

 

2022 - 2023
Gordon B. Pye Dissertation Fellowship, MIT
2018 - 2020
Marco Fanno Ph.D. Fellowship, Unicredit & Universities Foundation, full-tuition and stipend scholarship
2015 - 2017
Bocconi Merit Awards, full-tuition scholarship