We study interactive situations in which players are boundedly rational. Each player, rather than optimizing given a belief about the other players' behavior, as in the theory of Nash equilibrium, uses the following choice procedure. She first associates one consequence with each of her actions by sampling (literally or virtually) each of her actions once. Then she chooses the action that has the best consequence. We define a notion of equilibrium for such situations and study its properties.

We study a simple model of the determination of the level of employment in which a capitalist decides how many workers to hire, and then bargains over the wage with those whom he hires. If the capitalist hires all the available workers, his position is weak since, in the event of a strike, he is unable to hire strike-breakers; for this reason he chooses to leave some workers ("involuntarily") unemployed. An increase in unemployment benefits which raises the cost of hiring strike-breakers affects the bargaining power of both capitalist and workers; under some conditions it leads to a reduction in unemployment. 1.

We study Hotelling's two-stage model of spatial competition, in which two firms first simultaneously choose locations in the unit interval, then simultaneously choose prices. Under Hotelling's assumptions (uniform distribution of consumers, travel cost proportional to distance, inelastic demand of one unit by each consumer) the price-setting subgames possess equilibria in pure strategies for only a limited set of location pairs. Because of this problem (pointed out independently by Vickrey (1964) and d'Aspremont et al. (1979)), Hotelling's claim that there is an equilibrium of the two-stage game in which the firms locate close to each other is incorrect. A result of Dasgupta and Maskin (1986) guarantees that each price-setting subgame has an equilibrium in mixed strategies. We first study these mixed strategy equilibria. We are unable to provide a complete characterization of them, although we show that for a subset of location pairs all equilibria are of a certain type. We reduce the problem of finding an equilibrium of this type to that of solving three or fewer highly nonlinear equations. At each of a large number of location pairs we have computed approximate solutions to the system of equations. Next, we use our analytical results and computations to study the equilibrium location choices of the firms. There is a unique (up to symmetry) subgame perfect equilibrium in which the location choices of the firms are pure; in it, the firms locate 0.27 from the ends of the market. At this equilibrium, the support of the subgame equilibrium price strategy is the union of two short intervals. Most of the probability weight is in the upper interval, so that this strategy is reminiscent of occasional sales by the firms. We also find a subgame perfect equilibrium in which each firm uses a mixed strategy in locations. In fact, in the class of strategy pairs in which the firms use the same mixed strategy over locations, and this strategy is symmetric about 0.5, there is a single equilibrium. In this equilibrium most of the probability weight of the common strategy is between 0.2 and 0.4, and between 0.6 and 0.8. There is a wide range of pure Nash (as opposed to subgame perfect) equilibrium location pairs: the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close.

We consider a planner who chooses between two public policies and ask whether a referendum or a cost benefit analysis leads to higher welfare. We find that a referendum leads to higher welfare than a cost benefit analysis in a “common value” environment. Cost benefit analysis is better in a “private value” environment.

This note corrects an error in an example in Meetings with Costly Participation (AER 90(4), 927-943). It characterizes the set of equilibria for the example under the assumptions in the paper, shows that in all the equilibria an interval of moderate po- sitions is devoid of participants, and provides assumptions under which the result as originally stated is correct.

We study a collective decision-making process in which people interested in an issue may participate, at a cost, in a meeting, and the resulting decision is a compromise among the participants' preferences. We show that the equilibrium number of participants is small and their positions are extreme, and when the compromise is the median, the outcome is likely to be random. The model and its equilibria are consistent with evidence on the procedures and outcomes of U.S. regulatory hearings.