Working papers

Racing with a rearview mirror: innovation lag and investment dynamics, with Nicolas Klein and Chantal Marlats

We analyze a dynamic investment model in which short-lived agents sequentially decide how much to invest in a project of uncertain feasibility. The outcome of the project (success/failure) is observed after a fixed lag. We characterize the equilibrium and show that, in contrast with the case without lag, the unique equilibrium profile is not in threshold. If the initial belief is relatively high, investment decreases continuously as agents become more pessimistic about the feasibility of the innovation. Otherwise, investment is not monotonic in the public belief: players alternate periods of no investment and periods of positive, decreasing investment. The reason is that the outcome lag creates competition between a player and her immediate predecessors. A player whose predecessors did not invest may find investment attractive even if she is more pessimistic about the technology that her predecessors. We compare the total investment obtained in this equilibrium with that obtained with an alternative reward scheme where a mediator collects all the information about the players' experiences until some deadline, and split the payoff between all the players who obtained a success before the deadline.

Self-isolation under uncertainty, with Dominique Baril-Tremblay and Chantal Marlats

We analyze an epidemiological model where forward-looking individuals trade off the costs and benefits of self-isolation while being uncertain both about their type and about the dynamics of the epidemic. We characterize the unique interior symmetric equilibrium and identify the necessary conditions of the optimal solution. We calibrate our model to the COVID-19 pandemic and simulate the dynamics of the epidemic under various scenarios to illustrate the impact of uncertainty on self-isolation behaviors. We show that uncertainty may cause a second wave of infection and that the average level of social activity can decrease with the degree of uncertainty. Finally, uncertainty about the epidemic dynamics may be welfare improving, both in terms of fraction of deaths and average payoff.

The value of uncertainty for crowdfunding, with Alia Gizatulina, submitted.

A start-up firm sets up a crowdfinancing campaign to finance a new project. Investors decide whether to participate, anticipating that if the project succeeds, they can resell the project's token on a secondary market. We consider two types of firm: entrepreneur, which cares about the token's price dynamics, and scammer, which absconds with the money collected. The firm can reduce uncertainty for investors by undergoing a \textit{certification procedure} before posting the project. We prove the existence of a pooling equilibrium such that both types of firm choose the same price and thereby remain indistinguishable to investors but the crowdfunding market exists. Surprisingly, the average investor prefers an obfuscating certification procedure to a fully informative procedure and the entrepreneur type has strict incentives not to engage in any informative certification. Thus, our analysis justifies the introduction of a mandatory minimal disclosure policy for projects on crowdfunding platforms. 

Publications

Common knowledge in game theory, forthcoming in Revue Economique, special issue in honor of Robert Aumann.

When something is known to all and everybody knows that it is known to all, everybody knows that everybody knows that it is known to all and so on ad infinitum, this thing is said to be common knowledge. Aumann [1976] was the first to provide a formal characterization of the notion common knowledge in his celebrated article ``Agreeing to Disagree.'' This formalism has raised a number of exciting questions. Can commonly known individual differences in actions or beliefs be explained by asymmetric information? Do players need some sort of common knowledge to coordinate on some action profile? Can individuals achieve common knowledge by communicating? The purpose of this article is to review the work that has attempted to answer these questions.

Observation delays in teams and effort cycles, with Sid Gordon and Chantal Marlats, Games and Economic Behavior (2021) 130, 276-298.

This paper studies the dynamics of effort provision in teams when there are exogenous observation delays between partners. Agents are engaged in a common project whose duration is uncertain and yields no benefit until one of the agents has completed it. All it takes to complete the project is one success, which can be obtained after the investment of costly effort. An agent learns immediately when he succeeds, but learns whether his partners completed the project only after some exogenous delay. The main insight of the paper is that observation delays induce cyclical effort dynamics in equilibrium: Players alternate between periods in which they exert the maximal effort level and periods in which they make no effort at all. The size of the team has a negative impact on the average equilibrium effort, but a positive one on the players' payoff. Finally, introducing a small observation delay increases the average effort of patient players and makes them complete the project faster in expectation.

Strategic observation with exponential bandits, with Chantal Marlats, Journal of Economic Theory (2021) 193.

We introduce strategic observation into Keller, Rady and Cripps (2005)'s game of experimentation with conclusive breakthroughs. There are two players who must decide when to start and when to stop observation, given that observation is costly and stopping observation is irreversible. We construct a class of symmetric Markov Perfect Equilibria in which, on path, players fully experiment before starting observation, and allocate only a fraction of the resource to the risky arm afterwards. Each equilibrium in this class outperforms the symmetric equilibrium of Keller, Rady and Cripps (2005) in terms of payoffs.

Self-isolation, with Dominique Baril-Tremblay and Chantal Marlats, Journal of Mathematical Economics (2021) 93. (corrected version)

We analyze the spread of an infectious disease in a population when individuals strategically choose how much time to interact with others. Individuals are either of the severe type or of the asymptomatic type. Only severe types have symptoms when they are infected, and the asymptomatic types can be contagious without knowing it. In the absence of any symptoms, individuals do not know their type and continuously tradeoff the costs and benefits of self-isolation on the basis of their belief of being the severe type. We show that all equilibria of the game involve social interaction, and we characterize the unique equilibrium in which individuals partially self-isolate at each date. We calibrate our model to the COVID-19 pandemic and simulate the dynamics of the epidemic to illustrate the impact of some public policies.

Pre-play communication in procurement auctions: silence is not golden. Journal of Mathematical Economics, (2017) 71, 1-13.

I study the effect of cheap talk between bidders on the outcome of a first-price procurement auction in which participation is costly. Although no side payments or commitments are allowed, there exists a family of equilibria in which sellers use communication to collude on a subset of participants and/or reveal information about their cost. Cheap talk matters in the sense that it strictly enlarges the set of Nash equilibria (symmetric and asymmetric) and the set of public correlated equilibria of the game. I show that the buyer may benefit from cheap talk between sellers and that the surplus increases in the amount of information revealed in equilibrium under one fairly general condition. This is because when communication is cheap, sellers cannot directly collude on higher prices. Rather, communication leads to competition between fewer, but more aggressive bidders, which entails greater allocative efficiency and a decrease in the total wasteful entry cost. 

Communication, consensus, and order. Who wants to speak first?, (with Nicolas Houy), Journal of Economic Theory, (2008) 143 (1), 140-152.

Parikh and Krasucki [1990] show that, in a group of rational agents, communication of the value of a function f leads to a consensus on the value of f, provided some conditions on the communication protocol and the function f hold. In this article, we address the issue of the influence of the protocol on the outcome of the communication process, when agents value information positively. We show that, if it is common knowledge in a group of agents that some of them disagree on two protocols, then the consensus value of f must be the same for both protocols.  

Consensus and common knowledge of an aggregate of decisions, Games and Economic Behavior, (2008) 62, 722-731.

McKelvey and Page [1986] generalized Aumann’s [1976] agreement theorem to the case where agents have common knowledge of a statistic of their posterior probabilities of some event. They showed that if individuals have the same prior, and if the statistic satisfies a stochastic regularity condition, then common knowledge of it implies equality of all posteriors. We show a similar result in a more general setting where agents have common knowledge of a statistic of their individual decisions. Decisions can be posteriors as well as discrete actions such as buy or sell. We show that if the decision rule followed by individuals is balanced union consistent, and if the statistic of individual decisions is exhaustive, then common knowledge of it implies equality of all decisions. We give an example showing that neither Cave’s [1983] union consistency condition nor Parikh and Krasucki’s [1990] convexity condition are sufficient to guarantee the result.

Communication, consensus, and order: an extension with Bayesian agents, Mathematical Social Sciences, (2006) 51, 274-279. 

Parikh and Krasucki [1990] showed that pairwise communication of the value of a function f leads to a consensus about the communicated value if the function f is convex. They showed that union consistency of f may not be sufficient to guarantee consensus in any communication protocol. Krasucki [1996] proved that consensus occurs for any union consistent function if the protocol contains no cycle. We show that if agents communicate their optimal action, namely the action that maximizes their expected utility, then consensus obtains in any fair protocol for any action space.

Connaissance commune et consensus, Revue d’Economie Industrielle, (2006) 114 (1), 41-66.   (survey paper on common knowledge, in French)

Fondements épistémiques de concepts d’équilibre en théorie des jeux, (with Olivier Tercieux) Revue d’Economie Industrielle,  (2006) 114 (1) 67-84.  (survey paper on epistemic foundations of equilibrium concepts in game theory, in French)

Work in progress

Cheap talk in competitive bidding models with private and common value, with Françoise Forges

Learning through selling, with Alia Gizatulina

Learning to agree, with Nicolas Klein

Oldies in interactive epistemology

PhD Dissertation (In English with an extended abstract in French): Communication, common knowledge, and consensus.