# Working Papers

**Learning while Trading: Experimentation and Coasean Dynamics**

**Abstract.** I study a dynamic bilateral bargaining problem with incomplete information where better outside opportunities may arrive during negotiations. Gains from trade are uncertain. In a good-match market environment, outside opportunities are not available. In a bad-match market environment, superior outside opportunities stochastically arrive for either or both parties. The two parties begin their negotiations with the same belief on the type of the market environment. As arrivals are public information, learning about the market environment is common. One party, the seller, makes price offers at every instant to the other party, the buyer. The seller has no commitment power and the buyer is privately informed about his own valuation. This gives rise to rich bargaining dynamics. In equilibrium, there is either an initial period with no trade or trade starts with a burst. Afterward, the seller screens out buyers one by one as uncertainty about the market environment unravels. Delay is always present, but it is inefficient only if valuations are interdependent. Whether prices increase or decrease over time depends on which party has a higher option value of learning. The seller exercises market power. In particular, when the seller can clear the market in finite time at a positive price, prices are higher than the competitive price. However, market power need not be at odds with efficiency. Applications include durable-good monopoly without commitment, wage bargaining in markets for skilled workers, and takeover negotiations.

**Sequential Collective Search in Networks**

**Abstract. **I study social learning in networks where rational agents act in sequence, observe the choices of their connections, and acquire private information via costly sequential search. I characterize perfect Bayesian equilibria of the model by linking individual search policies to the probability that agents select the best action. The information structure of the model precludes information aggregation via martingale convergence arguments. If (and only if) search costs are not bounded away from zero, an improvement principle holds although the inferential challenge significantly differs from that of the standard model with exogenous private signals. I use this principle to show that asymptotic learning obtains in well–connected networks where information paths are identifiable. When search costs are bounded away from zero, even the weaker notion of maximal learning fails, except in ad hoc network topologies. Networks where agents observe random numbers of immediate predecessors share many equilibrium properties with the complete network, including the rate of convergence and the probability of wrong herds. Transparency of past histories has implications for welfare and efficiency. The simple policy intervention of letting agents observe the relative fraction of previous choices reduces inefficiencies and welfare losses.

# Work in Progress

**Dynamic Foundations for Static Empirical Models of Strategic Interaction **(with Lorenzo Magnolfi and Camilla Roncoroni)

**Abstract.** We propose the use of Bayes correlated equilibrium (BCE) as a restriction on cross-sectional outcomes when data are interpreted as the long-run result of a history of game plays. The structural parameters of agents’ payoff functions are partially identified under asymptotic no-regret (ANR), a minimal behavioral assumption describing an optimality condition for the long-term outcome of agents’ interaction. We establish the result in two steps. First, we prove that the time average of play that satisfies ANR converges to the set of ε-BCE of the underlying static game. Second, we show how to use the limiting model to obtain consistent estimates of the parameters of interest.

**Relational Learning Dynamics** (with Martin Peitz and Emanuele Tarantino)

**Abstract.** We study how self-enforcing repeated relationships between a principal and multiple competing agents form and evolve over time in the presence of learning. The principal combines transfers (compensation) and non-monetary tools (replacement threat) to motivate the agents to engage in costly experimentation with innovative activities. Agents know whether innovation opportunities are available in each period, whereas the principal does not. Monitoring is imperfect (and public), but agents’ strategies are private. Successful experimentation reduces the information asymmetry and parties become better able to specify the details of their cooperation in a relational contract. We characterize optimal incentive provision in two distinct market configurations: a deep market, with many agents, and a narrow market, where only two agents are available. Applications include managerial compensation and CEO rotation in innovative industries, and moral hazard problems in political economy.

**Competitive Experimentation with Heterogeneous Learning Modes** (with Francesco Paolo Conteduca)

**Abstract.** We study the role of diverse learning skills in games of competitive experimentation (e.g., an R&D race). We find that heterogeneous innovation abilities across competitors strongly affect the type and the magnitude of the inefficiencies that arise in equilibrium. As a consequence, industrial policies targeting inefficiencies in R&D should take into account the asymmetry in the firms’ learning process not to be detrimental.