Juan F. Escobar

Restricted feedback in long term relationships

This paper studies long term relationships, modeled as repeated games, with restricted feedback. Players condition current play on summary statistics of past play rather than the entire history, as may be the case in online markets. Our state strategy equilibrium framework allows for arbitrary restrictions on strategies. We derive a recursive characterization for the set of equilibrium payoffs similar to that of Abreu, Pearce, and Stacchetti (1986, 1990) [2,3] for perfect public equilibria and show that the set of equilibrium payoffs is the largest fixed point of a monotone operator. We use our characterization to derive necessary and sufficient conditions for efficient trade in a repeated product choice game where costumers condition their purchase decisions only on the last performance signal.

Equilibrium Analysis for a Network Market Model

In this paper we model and analyze a market equilibrium structure working on a network. The model is motivated by competition in electricity power generation markets, where consumers and producers are located in different nodes connected by power transmission lines. We analyze two different equilibrium concepts, namely, the Walrasian and the noncooperative Nash outcomes. By using concepts coming from Variational Analysis and Game Theory, we prove that both equilibria exist. Our existence proofs rely on fixed point theorems and epiconvergence stable approximations.

Monopolistic Competition in Electricity Networks

This paper models an electricity market with generators and customers located on a network. Generators bid cost functions and are dispatched by a system operator that minimizes the system cost while considering network constraints. We prove the existence of equilibrium and show that transmission constraints render the market imperfectly competitive. It is shown that competition among generators is similar to the interaction among firms in a monopolistic competition setting. A lower bound for market prices is obtained. Our results provide insights not captured by previous models. At a methodological level, we generalize standard oligopoly theory tools by using stability analysis.

Cooperation dynamics in repeated games of adverse selection

We study repeated games with Markovian private information and characterize op- timal equilibria as players become arbitrarily patient. We show that seemingly non-cooperative actions may occur in equilibrium and serve as signals of changes in private information. Play- ers forgive such actions, and use the information they convey to adjust their continuation play. However, to forgive is not to forget: players keep track of the number of aggressions and enter into a punishment phase if that number becomes suspiciously high. Our model explains features of long-run relationships that are only barely understood, such as equilibrium defaults, unilateral price cuts, collusive price leadership, graduated sanctions, and restitutions. We also explore a model in which interactions are frequent and show how increasing the persistence of the process of types reduces informational frictions.