Information and Equilibrium

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This grant supports research on four topics in microeconomic theory. The first two projects questions investigate aspects of "learning in games." This theory is based on the idea that equilibrium in games arises as the result of repeated observations leading players to have common forecasts of opponents' play; it is one of the primary justifications for the widespread use of game-theoretic equilibrium concepts in analyzing economic problems. Most past work on learning in games has assumed that at the end of each round of play, all players observe everyone's actions, which means for examples that bidders in a sealed-bid auction get to see all of the bids, and not just the winning one. The first project relaxes this assumption, and studies the possible long-run outcomes of learning processes in games when players get less information about what the other players have been doing. A second, and related, project studies the interpretation of games of incomplete information from the "learning in games" viewpoint. A particular focus of the project is to question the plausibility of the solution concept "Nash equilibrium without a common prior," which has been used in an increasing number of economic analyzes in recent years. The third project uses equilibrium analysis to study the conditions under which two competing auction houses for the same goods can both survive, as seems to be the case with Christie's and Sotheby's, and when the larger market will squeeze out the smaller one, as some conjecture that Ebay will do to its rivals. A preliminary insight is that buyers may be willing to patronize a market where prices tend to be higher if the variance of the price is higher as well. The fourth project studies the equilibria of infinitely repeated games with private but almost-public information and communication. Simpler models of infinitely repeated games, such as the repeated version of the "prisoner's dilemma" are widely used in economics and other social sciences, the project will extend this analysis to some cases where players only get imperfect and private signals of one another's actions- for example a firm might get evidence of a rival's secret price cuts from an unexpected loss of orders.