This paper establishes existence of a stationary Markov perfect equilibrium in general stochastic games with noise—a component of the state that is nonatomically distributed and not directly affected by the previous period's state and actions. Noise may be simply a payoff-irrelevant public randomization device, delivering known results on the existence of correlated equilibrium as a special case. More generally, noise can take the form of shocks that enter into players' stage payoffs and the transition probability on states. The existence result is applied to a model of industry dynamics and to a model of dynamic electoral competition.

Allowing for incomplete information, this paper characterizes the social choice functions that can be approximated by the equilibrium outcomes of a mechanism: incentive compatibility is necessary and almost sufficient for virtual Bayesian implementability. In conjunction with a second condition, Bayesian incentive consistency, incentive compatibility is also sufficient. This new condition is weak--under standard topological and informational assumptions it is satisfied by every social choice function. The type sets of the agents are taken to be arbitrary (possibly infinite) measurable spaces. An example shows that there are virtually (in fact, exactly) Bayesian implementable social choice functions that are not virtually implementable in iteratively undominated strategies.

We provide simple mechanisms to implement the efficient allocation of pollution, first assuming complete information across firms and then allowing for incomplete information. Both mechanisms operate by inducing firms to monitor one another, using firms’ reports to determine pollution allotments and transfers. The complete information mechanism determines a firm’s transfer according to a linear pollution price, set by other firms. Both mechanisms can be modified to be budget-balanced, in and out of equilibrium. The complete information mechanism implements the efficient allocation even when firms are allowed to use mixed strategies. Under a “single-crossing” condition, the same holds for the incomplete

We survey the literature on dynamic elections in the traditional settings of spatial preferences and rent seeking under perfect and imperfect monitoring of politicians. We define stationary electoral equilibrium, which encompasses notions used by Barro (1973), Ferejohn (1986), Banks and Sundaram (1998), and others. We show that repeated elections mitigate the commitment problems of politicians and voters, and that a responsive democracy result holds under general conditions. Term limits, however, attenuate the responsiveness finding. We also touch on related applied work, and we point to areas for fruitful future research, including the connection between dynamic models of politics and economics.