I study ultimatum bargaining with imperfectly observed offers. Imperfectly observed offers must be rejected with positive probability, even when the players’ preferences are common knowledge. Noisier observations imply a greater risk of rejection. In repeated ultimatum bargaining, the responding party can obtain a positive payoff if his signal of the opponent’s offer is also observed by the opponent herself, but not if his signal is private. In alternating-offers bargaining, a player is better off when her own offers are observed more precisely and her opponent’s offers are observed less precisely. Possible applications include international relations, regulation, principal-agency, and product quality provision.

I develop a simple model of social learning in which players observe others’ outcomes but not their actions. A continuum of players arrives continuously over time, and each player chooses once-and-for-all between a safe action (which succeeds with known probability) and a risky action (which succeeds with fixed but unknown probability, depending on the state of the world). The actions also differ in their costs. Before choosing, a player observes the outcomes of K earlier players. There is always an equilibrium in which success is more likely in the good state, and this alignment property holds whenever the initial generation of players is not well informed about the state. In the case of an outcome-improving innovation (where the risky action may yield a higher probability of success), players take the correct action as K → ∞. In the case of a cost-saving innovation (where the risky action involves saving a cost but accepting a lower probability of success), inefficiency persists as K → ∞ in any aligned equilibrium. Whether inefficiency takes the form of under-adoption or over-adoption also depends on the nature of the innovation. Convergence of the population to equilibrium may be nonmonotone.

This paper studies optimal dynamic tax policy under the threat of political reform. A policy will be reformed ex post if a large enough coalition of citizens supports reform; thus, sustainable policies are those that will continue to attract enough political support in the future. We find that optimal marginal capital taxes are either progressive or U-shaped, so that savings are subsidized for the poor and/or the middle class but are taxed for the rich. U-shaped capital taxes always emerge when individuals' political behavior is purely determined by economic motives.

We propose a model of cycles of conflict and distrust. Overlapping generations of agents from two groups sequentially play coordination games under incomplete information about whether the other side consists of bad types who always take bad actions. Good actions may be misperceived as bad and information about past actions is limited. Conflict spirals start as a result of misperceptions but also contain the seeds of their own dissolution: Bayesian agents eventually conclude that the spiral likely started by mistake, and is thus uninformative of the opposing group's type. The agents then experiment with a good action, restarting the cycle.

We study anonymous repeated games where players may be “commitment types” who always take the same action. We establish a stark anti-folk theorem: if the distribution of the number of commitment types satisfies a smoothness condition and the game has a “pairwise dominant” action, this action is almost always taken. This implies that cooperation is impossible in the repeated prisoner's dilemma with anonymous random matching. We also bound equilibrium payoffs for general games. Our bound implies that industry profits converge to zero in linear-demand Cournot oligopoly as the number of firms increases.