Articles scientifiques

A primal condition for approachability with partial monitoring


Journal of Dynamics and Games

juillet 2014, vol. 1, n°3, pp.447-469

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

Mots clés : Approachability theory, Online learning, Imperfect monitoring, Partial monitoring, Signals

In approachability with full monitoring there are two types of conditions that are known to be equivalent for convex sets: a primal and a dual condition. The primal one is of the form: a set C is approachable if and only all containing half-spaces are approachable in the one-shot game. The dual condition is of the form: a convex set C is approachable if and only if it intersects all payoff sets of a certain form. We consider approachability in games with partial monitoring. In previous works [5,7] we provided a dual characterization of approachable convex sets and we also exhibited efficient strategies in the case where C is a polytope. In this paper we provide primal conditions on a convex set to be approachable with partial monitoring. They depend on a modified reward function and lead to approachability strategies based on modified payoff functions and that proceed by projections similarly to Blackwell's (1956) strategy. This is in contrast with previously studied strategies in this context that relied mostly on the signaling structure and aimed at estimating well the distributions of the signals received. Our results generalize classical results by Kohlberg [3] (see also [6]) and apply to games with arbitrary signaling structure as well as to arbitrary convex sets

Analogies and Theories: The Role of Simplicity and the Emergence of Norms


Games and Economic Behavior

janvier 2014, vol. 83, pp.267–283

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

Mots clés : Case-based reasoning, Rule-based reasoning, Model selection, Social norms, Equilibrium selection

We consider the dynamics of reasoning by general rules (theories) and by specific cases (analogies). When an agent faces an exogenous process, we show that, under mild conditions, if reality happens to be simple, the agent will converge to adopt a theory and discard analogical thinking. If, however, reality is complex, analogical reasoning is unlikely to disappear. By contrast, when the agent is a player in a large population coordination game, and the process is generated by all players' predictions, convergence to a theory is much more likely. This may explain how a large population of players selects an equilibrium in such a game, and how social norms emerge. Mixed cases, involving noisy endogenous processes are likely to give rise to complex dynamics of reasoning, switching between theories and analogies

Beware of black swans: Taking stock of the description-experience gap in decision under uncertainty


Marketing Letters

septembre 2014, vol. 25, n°3, pp.269-280

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

Mots clés : Ambiguity Black swans Description-based decision making Fourfold pattern Probabilistic choices Risk

Uncertainty pervades most aspects of life. From selecting a new technology to choosing a career, decision makers rarely know in advance the exact outcomes of their decisions. Whereas the consequences of decisions in standard decision theory are explicitly described (the decision from description (DFD) paradigm), the consequences of decisions in the recent decision from experience (DFE) paradigm are learned from experience. In DFD, decision makers typically overrespond to rare events. That is, rare events have more impact on decisions than their objective probabilities warrant (overweighting). In DFE, decision makers typically exhibit the opposite pattern, underresponding to rare events. That is, rare events may have less impact on decisions than their objective probabilities warrant (underweighting). In extreme cases, rare events are completely neglected, a pattern known as the 'Black Swan effect.' This contrast between DFD and DFE is known as a description-experience gap. In this paper, we discuss several tentative interpretations arising from our interdisciplinary examination of this gap. First, while a source of underweighting of rare events in DFE may be sampling error, we observe that a robust description-experience gap remains when these factors are not at play. Second, the residual description-experience gap is not only about experience per se but also about the way in which information concerning the probability distribution over the outcomes is learned in DFE. Econometric error theories may reveal that different assumed error structures in DFD and DFE also contribute to the gap

Economic Models as Analogies


Economic Journal

août 2014, vol. 124, n°578, pp.513-533

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

People often wonder why economists analyze models whose assumptions are known to be false, while economists feel that they learn a great deal from such exercises. We suggest that part of the knowledge generated by academic economists is case-based rather than rule-based. That is, instead of offering general rules or theories that should be contrasted with data, economists often analyze models that are “theoretical cases”, which help understand economic problems by drawing analogies between the model and the problem. According to this view, economic models, empirical data, experimental results and other sources of knowledge are all on equal footing, that is, they all provide cases to which a given problem can be compared. We offer complexity arguments that explain why case-based reasoning may sometimes be the method of choice and why economists prefer simple cases

Eliciting Prospect Theory When Consequences Are Measured in Time Units: "Time Is Not Money"


Management Science

juillet 2014, vol. 60, n°7, pp.1844-1859

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

Mots clés : time risk; expected utility; prospect theory; reference point; utility; probability weighting; decision weights; loss aversion

We elicited the prospect theory components (utility, probability weighting, and loss aversion) when consequences are expressed as the time dedicated to a specific task or activity. A similar elicitation was performed for monetary consequences to allow an across-attribute (time/money) comparison of the elicited components (at the individual level). We obtained less concave utility and smaller loss aversion for time than for money. Moreover, while the probability weighting was predominantly inverse S-shaped for both attributes, it was less sensitive to probabilities and more elevated for time than for money. This finding implies more optimism for gains and more pessimism for losses