Working papers results

2020 - n° 658
We study the interplay between information acquisition and signaling. A sender decides whether to learn his type at a cost prior to taking a signaling action. A receiver responds after observing the signaling action. In the benchmark model where the sender's information acquisition decision is observed the sender does not acquire information and, therefore, does not signal. A rationale for signaling is provided by the model in which information acquisition is covert. There, in the unique equilibrium outcome surviving a form of never weak best response refinement the sender does acquire information and signals when the information is cheap.

Mehmet Ekmekci and Nenad Kos
Keywords: Signaling, information acquisition, refinements
2019 - n° 657
We relate two representations of the cost of acquiring information: a cost that depends on the experiment performed, as in statistical decision theory, and a cost that depends on the distribution of posterior beliefs, as in the theory of rational inattention. In many cases of interests, the two representations prove to be inconsistent with each other. We provide a systematic analysis of the inconsistency, propose a way around it, and apply our findings to information acquisition in games.
Tommaso Denti, Massimo Marinacci, and Aldo Rustichini
2019 - n° 656
We add here another layer to the literature on nonatomic anonymous games started with the 1973 paper by Schmeidler. More specifically, we define a new notion of equilibrium which we call '-estimated equilibrium and prove its existence for any positive '. This notion encompasses and brings to nonatomic games recent concepts of equilibrium such as self-confirming, peer-confirming, and Berk-Nash. This augmented scope is our main motivation. At the same time, our approach also resolves some conceptual problems present in Schmeidler (1973), pointed out by Shapley. In that paper the existence of pure-strategy Nash equilibria has been proved for any nonatomic game with a continuum of players, endowed with an atomless countably additive probability. But, requiring Borel measurability of strategy profiles may impose some limitation on players' choices and introduce an exogenous dependence among players' actions, which clashes with the nature of noncooperative game theory. Our suggested solution is to consider every suset of players as measurable. This leads to a nontrivial purely finitely additive component which might prevent the existence of equilibria and requires a novel mathematical approach to prove the existence of '-equilibria.
Simone Cerreia-Vioglio, Fabio Maccheroni, and David Schmeidler
2019 - n° 655
The allocation of bureaucrats across tasks constitutes a pivotal instrument for achieving an organization's objectives. In this paper, I measure the performance of World Bank bureaucrats by combining the universe of task assignment with an evaluation of task outcome and a hand-collected dataset of bureaucrat CVs. I introduce two novel stylized facts. First, bureaucrat performance correlates with task features and individual characteristics. Second, there exists a negative assortative matching between high-performing bureaucrats and low-performing countries. In the aftermath of natural disasters, which may weaken countries' performance even further, I observe that low-performing countries receive an additional allocation of high-performing bureaucrats. I discuss various interpretations of these findings.

Nicola Limodio
Keywords: Personnel Management, Public Sector, International Organizations
2019 - n° 654
We show that the incentive to engage in exclusionary tying (of two complementary products) may arise even when tying cannot be used as a defensive strategy to protect the incumbent's dominant position in the primary market. By engaging in tying, an incumbent firm sacrifices current profits but can exclude a more efficient rival from a complementary market by depriving it of the critical scale it needs to be successful. In turn, exclusion in the complementary market allows the incumbent to be in a favorable position when a more efficient rival will enter the primary market, and to appropriate some of the rival's efficiency rents. The paper also shows that tying is a more profitable exclusionary strategy than pure bundling, and that exclusion is the less likely the higher the proportion of consumers who multi-home.

Chiara Fumagalli and Massimo Motta
Keywords: Inefficient foreclosure, Tying, Scale economies, Network Externalities
2019 - n° 653
We report on a laboratory experiment measuring the preferences of a unique pool of risk professionals over various sources of uncertainty that entail different degrees of complexity. We then compare these preferences with those of a control group composed of social science students to obtain a deeper understanding of the mechanisms driving behaviors under risk and ambiguity. We find that (1) ambiguity aversion is robust to subjects' degree of sophistication in probabilistic reasoning and background. (2) An association exists between attitudes toward ambiguity and compound risk for students/less sophisticated subjects, and is mainly explained by their attitudes toward complexity. Such an association does not exist for risk professionals/more sophisticated subjects. (3) The failure to reduce compound risk emerges as a sufficent, but not necessary, condition for ambiguity non-neutrality. These findings suggest that decision making under ambiguity cannot be reduced to decision making under risk.

Ilke Aydogan, Loϊc Berger, and Valentina Bosetti
Keywords: Ambiguity aversion, reduction of compound lotteries, non-expected utility, model uncertainty, model misspecification
2019 - n° 652
Two extensive game structures with imperfect information are said to be behaviorally equivalent if they share the same map (up to relabelings) from profiles of structurally reduced strategies to induced terminal paths. We show that this is the case if and only if one can be transformed into the other through a composition of two elementary transformations, commonly known as "Interchanging of Simultaneous Moves" and "Coalescing Moves/Sequential Agent Splitting."

Pierpaolo Battigalli, Paolo Leonetti, and Fabio Maccheroni
Keywords: Extensive game structure; behavioral equivalence; invariant transformations
2019 - n° 651
This paper proposes a new approach to factor modeling based on the long-run equilibrium relation between prices and related drivers of risk (integrated factors). We show that such relationship reveals an omitted variable in standard factor models for returns that we label as Equilibrium Correction Term (ECT). Omission of this term implies misspecification of every factor model for which the equilibrium (cointegrating) relation holds. The existence of this term implies short-run mispricing that disappears in the long-run. Such evidence of persistent but stationary idiosyncratic risk in prices is consistent with deviations from rational expectations. Its inclusion in a traditional factor model improves remarkably the performance of the model along several dimensions. Furthermore, the ECT -being predictive- has strong implications for risk measurement and portfolio allocation. A zero-cost investment strategy that consistently exploits temporary idiosyncratic mispricing earns an average annual excess return of 6.21%, mostly unspanned by existing factors.

Carlo A. Favero and Alessandro Melone
Keywords: Asset Pricing, Asset Returns, Equilibrium Correction Term, Dynamic Factor Structure
2019 - n° 650
This paper presents a model of selective exposure to information and an experiment to test its predictions. An agent interested in learning about an uncertain state of the world can acquire information from one of two sources which have opposite biases: when informed on the state, they report it truthfully; when uninformed, they report their favorite state. When sources have the same reliability, a Bayesian agent is better off seeking confirmatory information. On the other hand, it is optimal to seek contradictory information if and only if the source biased against the prior is sufficiently more reliable. We test these predictions with an online experiment. When sources are symmetrically reliable, subjects are more likely to seek confirmatory information but they listen to the other side too frequently. When sources are asymmetrically reliable, subjects are more likely to consult the more reliable source even when prior beliefs are strongly unbalanced and listening to the less reliable source is more informative. Moreover, subjects follow contradictory advice sub-optimally; are too trusting of information in line with a source bias; and too skeptic of information misaligned with a source bias. Our experiment suggests that biases in information processing and simple heuristics - e.g., listen to the more reliable source - are important drivers of the endogenous acquisition of information.

Salvatore Nunnari and Giovanni Montanari
Keywords: Choice under Uncertainty, Information Acquisition, Bayesian Updating, Selective Exposure, Confirmation Bias, Limited Attention, Online Experiment
2019 - n° 649
MIn many domains, committees bargain over a sequence of policies and a policy remains in effect until a new agreement is reached. In this paper, I argue that, in order to assess the consequences of veto power, it is important to take into account this dynamic aspect. I analyze an infinitely repeated divide-the-dollar game with an endogenous status quo policy. I show that, irrespective of legislators' patience and the initial division of resources, policy eventually gets arbitrarily close to full appropriation bythe veto player; that increasing legislators' patience or decreasing the veto player's ability to set the agenda makes convergence to this outcome slower; and that the veto player supports reforms that decrease his allocation. These results stand in sharp contrast to the properties of models where committees bargain over a single policy. The main predictions of the theory find support in controlled laboratory experiments.

Salvatore Nunnari
Keywords: Dynamic Legislative Bargaining; Distributive Politics; Standing Committees; Endogenous Status Quo; Veto Power; Markov Perfect Equilibrium; Laboratory Experiments