Trading Under Incomplete Information

My dissertation studies the impact of information in trading. The objective is to understand to what extent incomplete information determines equilibrium prices arid equilibrium quantities bought by each agent. The different chapters in the dissertation approach this problem studying different models and develop different methodologies in order to provide novel insights.;The first chapter studies trade in informationally rich environments. A continuum of agents trades a divisible asset. Agents' valuation for the asset is subject to idiosyncratic and common payoff shocks. The information structure of the agents is assumed to be Gaussian and symmetric across agents. Importantly, agents are allowed to observe an arbitrarily large number of signals and allow for an arbitrary variance-covariance matrix of signals and payoff shocks. Agents trade via demand function competition. I characterize the set of linear Nash equilibrium, and analyze its informational properties.;The characterization of the equilibrium provides an account on how the information structure determines the equilibrium outcome. The amount of information aggregated by the price is increasing in the correlation of signals across agents and increasing in the correlation of payoff shocks across agents. The distance between the equilibrium asset allocation and the efficient asset allocation is decreasing in both of these correlations. Inefficiencies arise when an agent observes two signals that have correlated noise terms between each other. If two signals have correlated noise terms, then an agent uses an individual signal to predict payoff shocks and to predict the realization of the noise in another signal. This dual role in the use of signals leads to inefficient outcomes.;The second chapter is joint work with Dirk Bergemann and Stephen Morris. We analyze demand function competition with a finite number of agents and private information. We show that the nature of the private information determines the market power of the agents and thus price and volume of equilibrium trade.;We establish our results by providing a characterization of the set of all joint distributions over demands and payoff states that can arise in equilibrium under any information structure, extending results of Bergemann and Morris (2013). In demand function competition, the agents condition their demand on the endogenous information contained in the price. We compare the set of feasible outcomes under demand function to the feasible outcomes under Cournot competition. We find that the first and second moments of the equilibrium distribution respond very different to the private information of the agents.;The third chapter is joint work with Dirk Bergemann and Stephen Morris. In an economy of interacting agents with both idiosyncratic and aggregate shocks, we examine how the information structure determines aggregate volatility. We show that the maximal aggregate volatility is attained in a noise free information structure in which the agents confound idiosyncratic and common components of the payoff state, and display excess response to the common component, as in Lucas (1972). The upper bound on aggregate volatility is linearly increasing in the variance of idiosyncratic shocks, for any given variance of aggregate shocks. Our results hold in a setting of symmetric agents with linear best responses and normal uncertainty. We show our results by providing a characterization of the set of all joint distributions over actions and states that can arise in equilibrium under any information structure. This tractable characterization, extending results in Bergemann and Morris (2013), can be used to address a wide variety of questions.