This paper addresses the question of nonmyopic strategic behavior in an MDP planning procedure which is terminated when the rate of adjustment in the quantity of the public good is below some prespecified threshold. The problem is formulated as a dynamic game in which utility functions are additively separable. It is shown that the game possesses perfect Nash equilibria whose outcomes are Pareto optima. Moreover, any individually rational Pareto optimum can be attained through one of these Nash equilibria. Strategies in these equilibria involve a rate of revision in the quantity of the public good that is equal to the threshold level and insures monotonic convergence of the procedure in finite time.
This paper explores the extent to which standard, general equilibrium analysis of Pareto optima and of competitive equilibria can be applied to environments with moral hazard and adverse selection problems.Allowing for lotteries, contracts with random components, we first establish that an adverse-selection insurance economy, a moral-hazard insurance economy, a signaling economy, and a private-information labor market economy are all special cases of a simple, general structure.We then show that techniques for characterizing Pareto optimal contracts as solutions to concave programming problems are useful and nice and appear to be broadly applicable; allowing for lotteries, we show how to characterize the optimal allocations for the adverse-selection insurance and labor market economies.We then show that standard existence and optimality theorems for competitive equilibria apply in the linear space containing lotteries if agents with characteristics which are distinct and privately observed at the time of initial trading enter the economy-wide resource constraints in a homogeneous way (other kinds of diversity are not critical).For economies with moral hazard which satisfy the homogeneity condition, competitive contract markets single out a subset of the optima and thus can be consistent with apparent unemployment and with a random allocation of labor supplied though all households are averse to risk.The adverse-selection insurance and signaling economies, however, do not satisfy the homogeneity condition and are difficult to decentralize efficiently with a price system.
[We characterize a seller's optimal scheme for the sale of an indivisible good to one of n risk averse buyers. We also compare certain commonly used schemes, such as the high bid and second bid auctions, under the hypothesis of risk aversion.]
[This paper considers the interpolation of percentiles when the value of the c.d.f. F(x) is specified at n points. Upper and lower bounds on the percentile are obtained assuming that data is generated by a unimodal density. Sharper bounds are derived when the average of the observations in each interval is given. In addition to improving the standard linear interpolation, our results indicate that much information can be gained by reporting group means as well as frequency counts.]
The anonymous interaction of large numbers of economic agents is a kind of noncooperative situation which is markedly different from small-numbers strategic conflict. The nonatomic game has been introduced as a model for these many-agent situations. This paper contains a precise definition of what it means for a nonatomic game to be the limit of a sequence of finite-player games, and a theorem which states when the limit of equilibria of finite-player games will be an equilibrium of the nonatomic limit game. This is analogous to theorems prompted by Edgeworth's conjecture in core theory.