Working papers results

We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation (see below picture) where pt (a; A) is the probability that alternative a is selected from the set A of feasible alternatives if t is the time available to decide, is a time dependent noise parameter measuring the unit cost of information, u is a time independent utility function, and a is an alternative-specific bias that determines the initial choice probabilities and possibly reflects prior information. Our axiomatic analysis provides a behavioral foundation of softmax (also known as Multinomial Logit Model when a is constant). Our neuro-computational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behavior. Jointly, the two approaches provide a thorough understanding of soft-maximization in terms of internal causes (neurophysiological mechanisms) and external effects (testable implications).

We study agents in a social network who receive initial noisy signals about a fundamental parameter and then, in each period, solve a robust non-parametric estimation problem given their previous information and the most recent estimates of their neighbors. The resulting robust opinion aggregators are characterized by simple functional properties: normalization, monotonicity, and translation invariance. These aggregators admit the linear DeGroot's model as a particular parametric specification. However, robust opinion aggregators allow for additional features such as overweighting/underweighting of extreme opinions, confirmatory bias, as well as discarding information obtained from sources perceived as redundant. We show that under this general model, it is still possible to link the long-run behavior of the opinions to the structure of the underlying network. In particular, we provide sufficient conditions for convergence and consensus and we offer some bounds on the rate of convergence. In some parametric cases, we derive the influence of the agents on the limit opinions and we stress how it depends on their centrality as well as on their initial signals. Finally, we study sufficient conditions under which a large society learns the true parameter while also highlighting why this property may fail.

Recent studies argue that major crises can have long lasting effects on individual behavior. While most studies focused on natural disasters, we explore the consequences of the global pandemic caused by a lethal influenza virus in 1918-19: the so-called "Spanish Flu". This was by far the worst pandemic of modern history, causing up to 100 million deaths worldwide. Using information about attitudes of respondents to the General Social Survey (GSS), we find evidence that experiencing the pandemic likely had permanent consequences in terms of individuals' social trust. Our findings suggest that lower social trust was passed on to the descendants of the survivors of the Spanish Flu who migrated to the US. As trust is a crucial factor for long-term economic development, our research offers a new angle from which to assess current health threats.

This paper describes price discovery and liquidity provision in a dynamic limit order market with asymmetric information and non-Markovian learning. Investors condition on information in both the current limit order book and also, unlike in previous research, on the prior order history when deciding whether to provide or take liquidity. Our analysis shows that the information content of the prior order history can be substantial. Surprisingly, the information content of equilibrium orders can differ from order direction and aggressiveness.

We study the role of perceived threats from cultural diversity induced by terrorist attacks and a salient criminal event on public discourse and voters' support for far-right parties. We first develop a rule which allocates Twitter users in Germany to electoral districts and then use a machine learning method to compute measures of textual similarity between the tweets they produce and tweets by accounts of the main German parties. Using the dates of the aforementioned exogenous events we estimate constituency-level shifts in similarity to party language. We find that following these events Twitter text becomes on average more similar to that of the main far-right party, AfD, while the opposite happens for some of the other parties. Regressing estimated shifts in similarity on changes in vote shares between federal elections we find a significant association. Our results point to the role of perceived threats on the success of nationalist parties.

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.

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.

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.

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.

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.