We extend the folk theorem of repeated games to two settings in which players' information about others' play arrives with stochastic lags. In our first model, signals are almost-perfect if and when they do arrive, that is, each player either observes an almost-perfect signal of period-t play...

This paper discusses the implications of learning theory for the analysis of games with a move by Nature. One goal is to illuminate the issues that arise when modeling situations where players are learning about the distribution of Nature's move as well as learning about the opponents'...

We argue that some, but not all, superstitions can persist when learning is rational and players are patient, and illustrate our argument with an example inspired by the Code of Hammurabi. The code specified an “appeal by surviving in the river†as a way of deciding whether an...

We show that the use of communications to coordinate equilibria generates a Nash-threats folk theorem in two-player games with “almost public†information. The results generalize to the <i>n</i>-person case. However, the two-person case is more difficult because it is not possible to sustain...

This essay discusses the field of behavioral economics, with a focus on the papers in <i>Advances in Behavioral Economics</i>. These papers show that there is a body of “behavioral facts†that is both economically significant and regular enough to be modeled. For the field to advance further,...

This paper studies the set of equilibrium payoffs in repeated games with long- and short-run players and little discounting. Because the short-run players are unconcerned about the future, each equilibrium outcome is constrained to lie on their static reaction (best-response) curves. The natural...

Forecasts are said to be calibrated if the frequency predictions are approximately correct. This is a refinement of an idea first introduced by David Blackwell in 1955. We show that “<i>K</i>-initialized myopic strategies†are approximately calibrated when <i>K</i> is large. These strategies first...

This paper studies the effect of randomness in per-period matching on the long-run outcome of non-equilibrium adaptive processes. If there are many matchings between each strategy revision, the randomness due to matching will be small; our question is when a very small noise due to matching has...

Players choose an action before learning an outcome chosen according to an unknown and history-dependent stochastic rule. Procedures that categorize outcomes, and use a randomized variation on fictitious play within each category are studied. These procedures are “conditionally...

Di erent discrete time triangular arrays representing a noisy signal of players' activities can lead to the same limiting di usion process yet lead to di erent limit equilibria. Whether the limit equilibria are equilibria of the limiting continuous time game depends on the limit properties of...