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Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

We revisit well-known models of learning in which a sequence of agents make a binary decision on the basis of a private signal and additional information. We introduce efficiency measures, aimed at capturing the speed of learning in such contexts. Whatever the distribution of private signals, we show that the learning efficiency is the same, whether each agent observes the entire sequence of earlier decisions, or only the previous decision. We provide a simple necessary and sufficient condition on the signal distributions under which learning is efficient. This condition fails to hold in many prominent cases of interest. Extensions are discussed.

Départements : Economie et Sciences de la décision, GREGHEC (CNRS), Finance

Equity crowdfunding has recently become available and is quickly expanding. Concerns have been raised that investors ('backers') may be following the crowd 'too much' and making investments ('pledges') based on past investments rather than private information. We construct a model of equilibrium rational herding where uninformed investors follow signals generated by in formed investors with private information and a public belief generated by all past pledges. We show that large investments provide positive public information about the project's quality, whereas periods of absence of investment provide negative information. An information cascade is shown to occur only if not enough positive signals are generated. We then empirically analyse a large number of pledges from a leading European equity crowdfunding platform. We show that a pledge is strongly affected by both the size of the most recent pledge, and the time elapsed since the most recent pledge. For pledges that are not adjacent in the order of arrivals, the correlation between their sizes is still positive, but after being separated by two or more intervening pledges the correlation is no longer statistically significant. The effects are strongest for less-informed investors, and in some specifications the effects are strongest at the early stage of a campaign. We find similar results in IV analysis. Results are consistent with our model and inconsistent with some alternative models

Mots clés : Equity Crowdfunding, Herding

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel which has a fixed and limited number of messages and is subject to exogenous noise. Imperfect communication entails a loss of payoff for the persuader. We establish an upper bound on the payoffs the persuader can secure by communicating through the channel. We also show that the bound is tight: if the persuasion problem consists of a large number of independent copies of the same base problem, then the persuader can achieve this bound arbitrarily closely by using strategies which tie all the problems together. We characterize this optimal payoff as a function of the information-theoretic capacity of the communication channel

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory.

Mots clés : Stochastic Independence, Probabilistic Independence, Bayesian Decision Theory, Savage

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Agents make predictions based on similar past cases. The notion of similarity is itself learnt from experience by "second-order induction": past cases inform agents also about the relative importance of various attributes in judging similarity. However, there may be multiple "optimal" similarity functions for explaining past data. Moreover, the computation of the optimal similarity function is NP-Hard. We offer conditions under which rational agents who have access to the same observations are likely to converge on the same predictions, and conditions under which they may entertain different probabilistic beliefs.

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

We argue that a precedent is important not only because it changes the relative frequency of a certain event, making it positive rather than zero, but also because it changes the way that relative frequencies are weighed. Specifically, agents assess probabilities of future events based on past occurrences, where not all of these occurrences are deemed equally relevant. More similar cases are weighed more heavily than less similar ones. Importantly, the similarity function is also learnt from experience by "second-order induction". The model can explain why a single precedent affects beliefs above and beyond its effect on relative frequencies, as well as why it is easier to establish reputation at the outset than to re-establish it after having lost it. Finally, we discuss more sophisticated forms of learning, by which similarity is defined not only on cases but also on attributes, and the importance of some attributes, learnt from the data by second-order induction, can also affect the perceived importance of other attributes.

Départements : Economie et Sciences de la décision

This paper shows that bailouts of private agents can optimally take the form of asset purchases, even if this also means paying off external asset holders, in the presence of borrowing constraints and asymmetric information on liquidity needs. The combination of these two ingredients make direct compensation through loans and/or net transfers imperfect. Thus, when more constrained agents are also more exposed to the asset, the compensation through asset purchases becomes desirable. Anticipating these purchases, private agents engage in a collective bet on the defaulting asset, leading to an equilibrium implicit guarantee, where even an intrinsically worthless asset can be traded at a positive price

Mots clés : Implicit guarantees, bailouts, capital ows, capital controls

Départements : Economie et Sciences de la décision

We depart from Savage’s (1954) common state space assumption and introduce a model that allows for a subjective understanding of uncertainty. Within the revealed preference paradigm, we uniquely identify the agent’s subjective state space via her preferences conditional on incoming information. According to our representation, the agent’s subjective contingencies are coarser than the analyst’s states; she uses an additively separable utility with respect to her set of contingencies; and she adopts an updating rule that follows the Bayesian spirit but is limited by her perception of uncertainty. We illustrate our theory with an application to the Confirmatory Bias.

Mots clés : understanding of uncertainty, subjective state space, non-Bayesian updating

Départements : Economie et Sciences de la décision

This paper revisits the ability of central banks to manage private sector's expectations depending on its credibility and how this affects the use of interest rate rules and pegs to achieve monetary policy objectives. When private agents can only provide limited incentives for the central bank to follow a policy, we show that resulting limited credibility allows a central bank to prevents the inflation from diverging by defaulting on past promises if necessary. As a result, the Taylor rule, when expected, anchors inflation expectations on a unique equilibrium path as long as the Taylor principle is satisfied. Finally, we also show that limited credibility restricts the impact of long-term interest rate pegs, so as to make current conditions less dependent on future policy changes.

Mots clés : Taylor principle, Credibility, Forward Guidance

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

We offer a model that combines and generalizes case-based decision theory and expected utility maximization. It is based on the premise that an agent looks ahead and assesses possible future scenarios, but may not know how to evaluate their likelihood and may not be sure that the set of scenarios is exhaustive. Consequently, she also looks back at her memory for past cases, and makes decisions so as to maximize a combined function, taking into account both scenarios and cases. We allow for non-additive set functions, both over future scenarios and over past cases, to capture (i) incompletely specified or unforeseen scenarios, (ii) ambiguity, (iii) the absence of information about counterfactuals, and (iv) some forms of case-to-rule induction ("abduction") and statistical inference. We axiomatize this model. Learning in this model takes several forms, and, in particular, changes the relative weights of the two forms of reasoning.


Département Economie et Sciences de la Décision

Campus HEC Paris
1, rue de la Libération
78351 Jouy-en-Josas cedex


Jeremy GHEZ

Economie - Sciences de la Décision

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