We study repeated games with frequent actions and frequent imperfect public signals, where the signals are aggregates of many discrete events, such as sales or tasks. The high-frequency limit of the equilibrium set depends both on the probability law governing the discrete events and on how many events are aggregated into a single signal. When the underlying events have a binomial distribution, the limit equilibria correspond to the equilibria of the associated continuous-time game with diffusion signals, but other event processes that aggregate to a diffusion limit can have a different set of limit equilibria. Thus the continuous-time game need not be a good approximation of the high-frequency limit when the underlying events have three or more possible values.

We consider two kinds of “outside opportunity” that a seller of an indivisible good might have: selling to a different buyer and consuming the good herself. In both models the seller is uncertain about the buyer's valuation, and becomes more pessimistic over time. When the seller becomes sufficiently pessimistic, she prefers the outside opportunity, so she will not bargain indefinitely with the current buyer. Despite the resulting finite-horizon nature of negotiations, the link between the buyer's willingness to accept an offer and the seller's eagerness to go “outside” generates multiple equilibria.