We examine the rational expectations equilibrium paths of the model of search and barter in Diamond's "Aggregate Demand Management in Search Equilibrium." For some initial positions, there are two equilibrium paths converging to different steady states, with the high-activity path Pareto-dominating the low-activity path. With some parameters there is also a continuum of equilibrium paths converging to another steady state. Moreover, there can be cycles that are equilibrium paths, even though the environment is stationary.

We characterize a generalization of discounted logistic choice that incorporates a parameter to capture different views the agent might have about the costs and benefits of larger choice sets. The discounted logit model used in the empirical literature is the special case that displays a “preference for flexibility” in the sense that the agent always prefers to add additional items to a menu. Other cases display varying levels of “choice aversion,” where the agent prefers to remove items from a menu if their ex ante value is below a threshold. We show that higher choice aversion, as measured by dislike of bigger menus, also corresponds to an increased preference for putting off decisions as late as possible.

This paper studies reputation effects in games with a single long-run player whose choice of stage-game strategy is imperfectly observed by his opponents. We obtain lower and upper bounds on the long-run player's payoff in any Nash equilibrium of the game. If the long-run player's stage-game strategy is statistically identified by the observed outcomes, then for generic payoffs the upper and lower bounds both converge, as the discount factor tends to 1, to the long-run player's Stackelberg payoff, which is the most he could obtain by publicly committing himself to any strategy.

Imagine that one player, the “incumbent” competes with several “entrants”. Each entrant competes only with the incumbent, but observes play in all contests. Previous work shows that, as more and more entrants are added, the incumbent's reputation may dominate play of the game, if the entrants are faced in sequence. We identify conditions under which similar results obtain when the entrants are faced simultaneously, and we find specifications in which adding more simultaneous entrants has a dramatically different effect. We also show that, with either sequential or simultaneous play, incumbents need not prefer the situation in which their reputations can and do dominate play to the “informationally isolated” case in which each entrant observes only play in its own contest.

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.

Justified communication equilibrium (JCE) is an equilibrium refinement for signaling games with cheap-talk communication. A strategy profile must be a JCE to be a stable outcome of nonequilibrium learning when receivers are initially trusting and senders play many more times than receivers. In the learning model, the counterfactual “speeches” that have been informally used to motivate past refinements are messages that are actually sent. Stable profiles need not be perfect Bayesian equilibria, so JCE sometimes preserves equilibria that existing refinements eliminate. Despite this, it resembles the earlier refinements D1 and NWBR, and it coincides with them in co-monotonic signaling games. (JEL C70, D82, D83, J23, M51)

We use machine learning to uncover regularities in the initial play of matrix games. We first train a prediction algorithm on data from past experiments. Examining the games where our algorithm predicts correctly, but existing economic models don’t, leads us to add a parameter to the best performing model that improves predictive accuracy. We then observe play in a collection of new “ algorithmically generated” games, and learn that we can obtain even better predictions with a hybrid model that uses a decision tree to decide game-by-game which of two economic models to use for prediction. (JEL C70, C91)

A principal specifies time paths of effort provision, task allocation, and knowledge transfer for a cash-constrained apprentice, who is free to walk away at any time. In the optimal contract the apprentice pays for training by working for low or no wages and by working inefficiently hard. The apprentice can work on both knowledge-complementary and knowledge-independent tasks. We study the optimal time path of effort distortions and their impact on the knowledge transfer, and analyze the effect of regulatory limits on the length of apprenticeships and on how much effort apprentices are allowed to provide. (JEL D82, D86, J24, J41, M53)

We introduce a new model of repeated games in large populations with random matching, overlapping generations, and limited records of past play. We prove that steady-state equilibria exist under general conditions on records. When the updating of a player’s record can depend on the actions of both players in a match, any strictly individually rational action can be supported in a steady-state equilibrium. When record updates can depend only on a player’s own actions, fewer actions can be supported. Here, we focus on the prisoner’s dilemma and restrict attention to strict equilibria that are coordination-proof, meaning that matched partners never play a Pareto-dominated Nash equilibrium in the one-shot game induced by their records and expected continuation payoffs. Such equilibria can support full cooperation if the stage game is either “strictly supermodular and mild” or “strongly supermodular,” and otherwise permit no cooperation at all. The presence of “supercooperator” records, where a player cooperates against any opponent, is crucial for supporting any cooperation when the stage game is “severe.”