Repeated Games with Asynchronous Monitoring

We study two modi…cations of the standard model of repeated games with public signals. In one modi…cation, players osberve an underlying public signal at random and privately known times, where the public signals are Poisson events and either the observations occur within a small epsilon time interval or the obsevations have an exponential waiting times. In the second modi…cation, the players observe the position of a di¤usion process with a small amount of noise. We show that in the Poisson cases the high-frequency limist are the same as in the Fudenberg and Levine [2007, 2008] study of high-frequency public signals, but that the limits can di¤er when the signals correspond to a di¤usion.