Research

Working papers

• Racing with a rearmirror: innovation lag and investment dynamics, with N. Klein and L.Ménager

We analyze a dynamic model in which investment decisions in a technology of uncertain quality must be made continuously over time. The outcome of the investments (success/failure) are realized after a fixed lag. We begin by examining the case of a single funding agency that decides, at each point in time, how much to invest in the technology. We show that, unlike the case without lag, where the optimal investment follows a threshold behavior, introducing lag leads to investment dynamics characterized by a wave-like pattern. Second, we analyze the case where a continuum of short-lived players make their investment decisions sequentially and compete to be the first to achieve a success. We show that when the lag is large enough, periods of positive investment indefinitely alternate with periods of no investment, resulting in an infinite series of lumpy investment waves. However, when the outcome lag is sufficiently short, but positive, equilibrium investment decreases gradually and smoothly over time along with beliefs, except at certain points where it exhibits a downward jump. The aggregate payoff, which aligns with the agency’s payoff, is strictly lower in equilibrium than in the agency's optimal solution if and only if there is a positive outcome lag. We show that these inefficiencies are not due to over- or under-investment, but rather result from the misallocation of investments over time.

• The value of information in times of epidemics, with D.Baril-Tremblay and L. Ménager

We analyze an epidemiological model where forward-looking individuals trade off the costs and benefits of social distancing while being uncertain both about the characteristics of the disease and thus about the dynamics of the epidemic. We characterize the unique interior symmetric equilibrium. We show that uncertainty can cause an infection rebound. We show on simulations that uncertainty about the characteristics of the disease may be welfare improving, both in terms of fraction of deaths and average payoff.  

Publications 

•  Observation delays and cycles (with Sidartha Gordon and Lucie Ménager) (2021), Games and Economic Behaviors, 130, pp276-298. 

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 Lucie Ménager) (2021),  Journal of Economic Theory, 193, 105232.  

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 

• Self-Isolation (with Dominique Baril-Tremblay and Lucie Ménager) (2021) Journal of Mathematical Economics, 93, 102483. 

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.

• Reputation in stochastic games with two long lived players, (2021) Economic Theory, 71(1), 1-31.

This paper extends the reputation result of Evans and Thomas (Econometrica 65(5):1153–1173, 1997) to stochastic games. Specifically, I analyze reputation effects with two long-lived (but not equally long) players in stochastic games, that is, in games in which the payoffs depend on a state variable and the law of motion for states is a function of the current state and of the players’ actions. The results suggest that reputation effects in stochastic games can be expected if the uninformed player has a weak control of the law motion or if there is no irreversibility. On the contrary, in economic situations with irreversibility and in which the uninformed player’s strong control of the transition, such as the hold-up problems, reputation effects are unlikely to be obtained.

• Perturbed finitely repeated games, Mathematical Social Sciences, 2019, vol. 98, p. 39-46.

This paper explores the robustness of predictions made in long but finitely repeated games. The robustness approach used in this paper is related to the idea that a modeler may not have absolute faith in his model: The payoff matrix may not remain the same at all dates and may vary temporarily from time to time with an arbitrarily small probability. Therefore, he may require not rejecting an outcome if it is an equilibrium in some game arbitrarily close to the original one. It is shown that the set of feasible and rational payoffs is the (essentially) unique robust equilibrium payoff set when the horizon is sufficiently large. Consequently, cooperation can arise as an equilibrium behavior in a game arbitrarily close to the standard prisoner’s dilemma if the horizon is finite but sufficiently long.

• A folk theorem for stochastic games with finite horizon, Economic Theory, 2015, vol. 58, no. 3.

This paper provides assumptions for a limit Folk theorem in stochastic games with finite horizon. In addition to the asymptotic assumptions à la Dutta (J Econ Theory 66:1–32, 1995 ) I present an additional assumption under which the Folk theorem holds in stochastic games when the horizon is long but finite. This assumption says that the limit set of SPE payoffs contains a state invariant payoff vector $w$ and, for each player $i$, another payoff vector that gives less than $w$ to $i$. I present two alternative assumptions, one on a finite truncation of the stochastic game and the other on stage games and on the transition function, that imply this assumption

•  Reputation Effects in a Hold-Up Problem, Revue économique, 2011, 62(3), 557-565.