# Job Market Papers

**Estimation of Games under No Regret **(with Lorenzo Magnolfi and Camilla Roncoroni)

**Abstract. **We develop a method to estimate a game’s primitives in complex dynamic environments. Because of the environment’s complexity, agents may not know or understand some key features of their interaction. Instead of equilibrium assumptions, we impose an asymptotic ε-regret (ε-AR) condition on the observed play. According to ε-AR, the time average of the counterfactual increase in past payoffs, had each agent changed each past play of a given action with its best replacement in hindsight, becomes small in the long run. We first prove that the time average of play satisfies ε-AR if and only if it converges to the set of Bayes correlated ε-equilibrium predictions of the stage game. Next, we use the static limiting model to construct a set estimator of the parameters of interest. The estimator’s coverage properties directly arise from the theoretical convergence results. The method applies to panel data as well as to cross-sectional data interpreted as long-run outcomes of learning dynamics. We apply the method to pricing data in an online marketplace. We recover bounds on the distribution of sellers’ marginal costs that are useful to inform policy experiments.

**A Mediator Approach to Mechanism Design with Limited Commitment** (with Takuro Yamashita)

**Abstract. **We study the role of information structures in mechanism design problems with limited commitment. In each period, a principal offers a “spot” contract to a privately informed agent without committing to future spot contracts, and the agent responds to the contract. In contrast to the classical approach in which the information structure is fixed, we allow for all admissible information structures. We represent the information structure as a fictitious mediator and re-interpret the model as a mechanism design problem by the mediator with commitment. The mediator collects the agent’s private information and then, in each period, privately recommends the principal’s spot contract and the agent’s response in an incentive-compatible manner (both in truth-telling and obedience). We provide several examples to identify why new equilibrium outcomes can arise once we allow for general information structures. We next develop a durable-good monopoly application. We show that trading outcomes and welfare consequences can substantially differ from those in the classical model with a fixed information structure. In the seller-optimal mechanism, the seller offers a discounted price to the high-valuation buyer only in the initial period, followed by the high, surplus-extracting price until some endogenous deadline, when the buyer’s information is revealed and hence fully extracted. As a result, the Coase conjecture fails: even in the limiting case of perfect patience, the seller makes a positive surplus, and the trading outcome is not the first best. We also characterize mediated and unmediated implementation of the seller-optimal outcome.

# Other Working Papers

**Collective Search in Networks **[SSRN] – **R&R at Games and Economic Behavior**

**Abstract. ** I study social learning in networks with information acquisition and choice. Bayesian agents act in sequence, observe the choices of their connections, and acquire information via sequential search. Complete learning occurs if search costs are not bounded away from zero and the network is sufficiently connected and has identifiable information paths. If search costs are bounded away from zero, complete learning is possible in many stochastic networks, including almost-complete networks, but even a weaker notion of long-run learning fails in many other networks. When agents observe random numbers of immediate predecessors, the rate of convergence, the probability of wrong herds, and long-run efficiency properties are the same as in the complete network. The density of indirect connections affects convergence rates. Network transparency has short-run implications for welfare and efficiency. Simply letting agents observe the shares of earlier choices reduces inefficiency and welfare losses.

**Learning while Bargaining: Experimentation and Coasean Dynamics **[slides] – new draft coming soon

- Best Graduate Paper Award at the Lisbon Meetings in Game Theory and Applications 2018
- Finalist for the LAGV Prize at ASSET 2018

**Abstract.** I study dynamic bargaining with one-sided incomplete information when superior outside options may arrive during negotiations. A seller makes price offers at every instant to a buyer. The seller has no commitment power, and the buyer is privately informed about his own valuation. Gains from trade are ex ante uncertain: in a good-match type of market, no outside option exists; in a bad-match type of market, outside options stochastically arrive for either or both parties. The two parties begin their negotiations with the same belief about the market type. Arrivals are public and learning about the market type is common. In equilibrium, either there is an initial period with no trade or trade starts with a burst. Afterward, the seller screens out buyer types one by one as uncertainty about the market type unravels. Delay is always present. It is efficient with independent private valuations. Instead, with (endogenously) interdependent valuations, the timing of agreements is inefficient. Inefficiently late and inefficiently early agreements can both arise as equilibrium outcomes. I link the type of inefficiency to the sign of the externality among the seller’s multiple selves. Whether prices increase or decrease over time depends on which party has a higher option value of waiting to learn. When the seller can clear the market in finite time at a positive price, prices are higher than the competitive price. This, however, need not be at odds with efficiency.

**Identification and Estimation in Search Models with Social Information** (with Emanuele Tarantino)

**Abstract.** We propose a theoretical analysis of the conditions under which estimates of search cost distributions are biased when Bayes rational agents search in the presence of social information. We extend the canonical empirical sequential and simultaneous search models by allowing a share of the agents in the population to observe the choice of one of their social connections. We find that social information changes agents’ optimal search decisions. We compute the estimator of search cost distributions under various standard datasets. We find that neglecting social information typically leads to biased and inconsistent estimates of search cost distributions, with the bias sign and magnitude depending on the dataset’s content. The bias magnitude is increasing in the share of agents in the population with social information. We also discuss offline estimation techniques, exogenous variations in the data, and partial identification approaches that are useful to recover correct estimates of search cost distributions.

# Selected Work in Progress

**Robust Identification in Repeated Games** (with Lorenzo Magnolfi) – coming soon

**Social Search: An Experimental Study** (with Maria Bigoni, Michela Boldrini, and Emanuele Tarantino)

**Information Design with Optimal Frame Choice** (with Yulia Evsyukova and Federico Innocenti)