Collaborative Research: New Informationally Robust Approaches to Mechanism Design and Games of Incomplete Information

University Of California-San Diego, La Jolla CA

Investigators

Abstract

This project develops new tools for robust predictions in strategic games where the outcome depends on some unobserved state of nature (although the players do not observe the realized state, they may receive signals allowing to update the likelihood of each possible state). These games are a fundamental tool in economic theory for understanding behavior in a wide range of settings, such as oligopoly, auctions, electoral competition, and bank runs. The classical approach is to study behavior under a fixed model of player’s information. In many practical settings, however, an analyst or policy maker may be concerned about misspecification of the players' information. The tools that we develop give predictions about the players' behavior and policy recommendations about market design, without relying on a full specification of the informational environment. The project has three components. First, we develop a new solution concept that characterizes rationalizable behavior under common prior beliefs about payoff relevant states. This is a generalization of the solution concept known as Bayes’ correlated equilibrium (BCE), replacing the usual Nash equilibrium with a weaker notion of interim correlated rationalizability. This is important, because in many settings (such as spectrum auctions which occur infrequently), strategic agents may not have had sufficient time or experience to converge on a Nash equilibrium; nevertheless, we can make non-trivial predictions about behavior based on the premise that actions are rational under some (not necessarily correct) beliefs. Second, we study a distinct generalization of BCE in which there is an upper bound on players’ information. This complements the lower bounds on information found in the existing formulations of BCE; and it allows us to obtain more realistic predictions in settings where agents do not have access to all payoff-relevant information (such as bank runs or auctions of "toxic" assets). Third, we extend and apply the burgeoning theory of informationally-robust optimal mechanisms to the problem of designing efficient trading mechanisms. Existing models of bilateral trade are primarily focused on the simple and stylized case where buyer and seller each know their respective values, and those values are statistically independent. Using the informationally-robust approach, we derive new trading mechanisms that are guaranteed to produce non-trivial gains from trade even when buyer and seller values are interdependent and information is correlated. The insights we develop about robust trading platforms could be utilized to improve efficiency in a wide variety of markets with informational frictions, such as the markets for financial securities or health insurance. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.