MICRO/THEORY: Games with Imperfectly Attributable Actions; Professor David Rahman (University of Minnesota)

Abstract:

I develop and apply dual recursive methods to study dynamic games with imperfectly attributable actions, meaning that, statistically, the behavior of different individuals can be indistinguishable. I begin by defining two kinds of perfect public equilibrium that exploit imperfect attribution differently, and then formulate sequence problems that realize their welfare as linear programs. Next, I equate their value functions as maximal fixed points of corresponding functional equations defined by convex programs, and use the dual functional equations to propose algorithms for computing equilibrium payoff sets. In continuous-time games with Brownian information, these algorithms produce welfare optimality (HJB) equations that relate the curvature of welfare to welfare itself. They also reveal the relationship between imperfect attribution, or, technically, a lack of pairwise identifiability, and viscosity solutions of welfare equations. I illustrate these results with an application to the repeated Prisoners' Dilemma.