Endogenous Monitoring in a Partnership Game,  American Economic Review, March 2020, 110(3): 776-796.  Full text I consider a repeated game in which, due to imperfect monitoring, no collusion can be sustained. I add a self-interested monitor who commits to generating an imperfect private signal of firms’ actions and sends a public message. The monitor makes an offer specifying the precision of the signal generated and the amount to be paid in return. I show that with low monitoring cost, collusive equilibria exist. In the monitor’s favorite collusive equilibrium, firms’ payoffs are decreasing in the discount factor. My model helps explain the cartel agreements between the mafia and firms in legal industries in Italy and America.

Optimally stubborn: how long to hold and who will fold?, Theoretical Economics, May 2026, 21(2): 402-433. Full text (Old version) Models on reputational bargaining have introduced a perturbation with simple behavioral types as a way of refining payoff predictions. I show that this outcome refinement is not robust to the specification of the behavioral type. More specifically, I propose a relaxation of the strategy restriction on behavioral types relative to the literature, allowing behavioral types to choose their initial demands. With this relaxation any feasible payoff can be achieved in equilibrium for the rational type when the probability of facing a behavioral type is small. My results highlight the implications of different perturbations for economic applications. 

Dynamic Screening of Buyers with Heterogeneous Purchase Frequency, Econometrica, July 2026, 94(4): 1245--1278, with Johannes Hörner (TSE, CNRS). Full text Online Appendix Supplementary Online Appendix   We consider a continuous-time game between a buyer and a seller. The buyer privately knows how often he needs to trade. When he does, he can choose to either engage with the seller, who chooses what utility to supply, or search for an alternative. Because time is informative, the seller learns and adjusts her behavior over time. Without commitment, in the Markov perfect equilibrium, the seller starts with a pooling offer, before experimenting with occasional separating offers. Her payoff is non-monotone –in fact, quasi-convex– in her belief about the buyer’s type. With commitment, the seller can take advantage of limited-time offers to extract all the buyer’s surplus. (previously circulated as Dynamic Screening: Why Weight isn’t Volume)

On the Role of Outside Options in Buyer-Seller Relationships, with Johannes Hörner (TSE, CNRS). Full text  Online Appendix 

We consider a buyer-seller relationship, in which due to private information and a lack of flexible transfers, cooperation cannot be sustained efficiently. In each round, the buyer either purchases from the seller or takes an outside option. The fluctuating outside option may be public or private information. The seller chooses what quality to supply. We find that the buyer initially forgoes mutually beneficial trades before then visiting more often than he would like to, myopically. Under private information, the relationship recurrently undergoes gradual self-reinforcing downturns when trust is broken and instantaneous recoveries when loyalty is shown. Transparency regarding the outside option benefits both buyer and seller. (previously circulated as Too much of a good thing?)

Reputational Spillovers, with Aditya Kuvalekar (Essex University). Accepted at EC'26 Full text We analyze a reputational bargaining game in which a central player negotiates simultaneously with two peripheral players. Each player may be a rational type or a commitment type that insists on a fixed share, and concessions are publicly observed. Because a player’s type is global across negotiations, reputational spillovers arise: behavior in one negotiation updates beliefs in the other. We show that these spillovers overtur bilateral benchmark of Abreu and Gul (2000). The central player may concede more and earn strictly less than a weaker partner. Peripheral players benefit most when the central player’s higher-stakes negotiation is elsewhere. 

Equilibrium Uniqueness in a Repeated Partnership Game. Full text This paper studies a repeated two-player partnership game with imperfect public monitoring and a binary public signal. Although each player's action changes the public-signal distribution, arbitrarily high patience need not support a perfect public equilibrium other than perpetual defection. I give primitive necessary and sufficient conditions under which perpetual defection is the unique perfect public equilibrium for every discount factor. The first condition rules out PPEs sustained through symmetric mixed action profiles and signal contingent continuation payoffs. The second rules out PPEs sustained through asymmetric action profiles and continuation-payoff differences across players.

Competition, Price Discrimination and the Returns to Search: A Theory of Frequent-Buyer Discounts. With Jim Dana (Northeastern) and Johannes Hörner (TSE, CNRS). Draft available on request. We show that customer loyalty programs, and more specifically, discounts for frequent buyers, are an outcome of price discrimination by firms in imperfectly competitive markets with costly consumer search. We analyze oligopoly models of both search goods and experience goods when consumers differ only in their purchase frequency. Consumers’ valuations are drawn from the same distribution and have identical search costs. However, because frequent buyers have greater incentives to search, in equilibrium they have better outside options, search more often, and have higher ex post expected valuations. Competing firms offer lower prices to frequent buyers, and when consumers’ purchase frequency is private information, they do so using loyalty programs or frequent buyer discounts. These consumers pay lower prices, even though in equilibrium they have greater gains from trade (higher valuations).

Looking Past the Price Tag. With Johannes Hörner (TSE, CNRS). We study dynamic buyer-seller interactions in an imperfectly competitive market with search frictions. Firms differ in their cost of production. Prices are publicly observable, but consumers must engage in costly search to discover their firm-specific match value. In the stationary equilibrium, firms initially sell for free to attract consumers, but as a firm builds up a customer base it eventually hikes its price. This process generates persistent price dispersion and firm size heterogeneity, with low cost firms becoming bigger and charging lower prices. Our model explains staggered price hikes, long-run price differences, and endogenous firm growth patterns.

Competition and Consumer Search.  With Jim Dana (Northeastern) and Johannes Hörner (TSE, CNRS). Draft available on request. We study a growing market in which consumers must pay a cost to learn whether a firm’s product is a good fit. Prices are publicly observed, but match quality is not. Consumers face repeated purchase opportunities that arrive as a Poisson process, and their match values are persistent. In equilibrium, firms initially offer the product for free and then hike their prices over the time, with monetization occurring at an increasing rate as the market matures. This endogenous acceleration lowers consumers’ outside option from re-entering search, amplifying firms’ market power. Firms that monetize earlier become smaller, “niche” providers charging higher prices, whereas firms that monetize later achieve larger scale and charge lower (though rising) prices. We characterize the equilibrium dynamics and derive testable predictions for the joint evolution of prices, churn, and firm size.

Bargaining with Multiple Partners. With Idione Meneghel (ANU). We analyze a model of bargaining with two sides, say buyers and sellers. Each agent wants to make exactly one deal. Each player can choose from multiple possible bargaining partners, and some may be a better match than others. We analyze how the presence of alternative bargaining partners affects the outcome of a bilateral bargaining agreement.