Two players announce bargaining postures to which they may become committed and then bargain over the division of a surplus. The share of the surplus that a player can guarantee herself under first-order knowledge of rationality is determined (as a function of her probability of becoming committed), as is the bargaining posture that she must announce in order to guarantee herself this much. This “maxmin” share of the surplus is large relative to the probability of becoming committed (e.g., it equals 30% if the commitment probability is 1 in 10 and equals 13% if the commitment probability is 1 in 1000), and the corresponding bargaining posture simply demands this share plus compensation for any delay in reaching agreement.

We study the problem of a partisan gerrymanderer who assigns voters to equipopulous districts to maximize his party's expected seat share. The designer faces both aggregate, district‐level uncertainty (how many votes his party will receive) and idiosyncratic, voter‐level uncertainty (which voters will vote for his party). Segregate‐pair districting , where weaker districts contain one type of voter, while stronger districts contain two, is optimal for the gerrymanderer. The optimal form of segregate‐pair districting depends on the designer's popularity and the relative amounts of aggregate and idiosyncratic uncertainty. When idiosyncratic uncertainty dominates, a designer with majority support pairs all voters, while a designer with minority support segregates opposing voters and pairs more favorable voters; these plans resemble uniform districting and “packing‐and‐cracking,” respectively. When aggregate uncertainty dominates, the designer segregates moderate voters and pairs extreme voters; this “matching slices” plan has received some attention in the literature. Estimating the model using precinct‐level returns from recent U.S. House elections shows that, in practice, idiosyncratic uncertainty dominates. We discuss implications for redistricting reform, political polarization, and detecting gerrymandering. Methodologically, we exploit a formal connection between gerrymandering—partitioning voters into districts—and information design—partitioning states of the world into signals.

We study reputation formation where a long‐run player repeatedly observes private signals and takes actions. Short‐run players observe the long‐run player's past actions but not her past signals. The long‐run player can thus develop a reputation for playing a distribution over actions, but not necessarily for playing a particular mapping from signals to actions. Nonetheless, we show that the long‐run player can secure her Stackelberg payoff if distinct commitment types are statistically distinguishable and the Stackelberg strategy is confound‐defeating . This property holds if and only if the Stackelberg strategy is the unique solution to an optimal transport problem. If the long‐run player's payoff is supermodular in one‐dimensional signals and actions, she secures the Stackelberg payoff if and only if the Stackelberg strategy is monotone. Applications include deterrence, delegation, signaling, and persuasion. Our results extend to the case where distinct commitment types may be indistinguishable, but the Stackelberg type is salient under the prior.

The majority of labor transactions throughout much of history and a significant fraction of such transactions in many developing countries today are “coercive,” in the sense that force or the threat of force plays a central role in convincing workers to accept employment or its terms. We propose a tractable principal–agent model of coercion, based on the idea that coercive activities by employers, or “guns,” affect the participation constraint of workers. We show that coercion and effort are complements, so that coercion increases effort, but coercion always reduces utilitarian social welfare. Better outside options for workers reduce coercion because of the complementarity between coercion and effort: workers with a better outside option exert lower effort in equilibrium and thus are coerced less. Greater demand for labor increases coercion because it increases equilibrium effort. We investigate the interaction between outside options, market prices, and other economic variables by embedding the (coercive) principal–agent relationship in a general equilibrium setup, and studying when and how labor scarcity encourages coercion. General (market) equilibrium interactions working through the price of output lead to a positive relationship between labor scarcity and coercion along the lines of ideas suggested by Domar, while interactions those working through the outside option lead to a negative relationship similar to ideas advanced in neo-Malthusian historical analyses of the decline of feudalism. In net, a decline in available labor increases coercion in general equilibrium if and only if its direct (partial equilibrium) effect is to increase the price of output by more than it increases outside options. Our model also suggests that markets in slaves make slaves worse off, conditional on enslavement, and that coercion is more viable in industries that do not require relationship-specific investment by workers.

We study how discounting and monitoring jointly determine whether cooperation is possible in repeated games with imperfect (public or private) monitoring. Our main result provides a simple bound on the strength of players' incentives as a function of discounting, monitoring precision, and on‐path payoff variance. We show that the bound is tight in the low‐discounting/low‐monitoring double limit, by establishing a public‐monitoring folk theorem where the discount factor and the monitoring structure can vary simultaneously.

We prove the folk theorem for discounted repeated games with anonymous random matching. We allow non‐uniform matching, include asymmetric payoffs, and place no restrictions on the stage game other than full dimensionality. No record‐keeping or communication devices—including cheap talk communication and public randomization—are necessary.