The authors derive necessary and sufficient conditions for a pair of functions to be the optimal policy function and the optimal value function of a dynamic maximization problem with convex constraints and concave objective functional. It is shown that every Lipschitz continuous function can be...

It has been known that, in aggregating infinite utility streams, there does not exist any social welfare function, which satisfies the axioms of Pareto, intergenerational equity, and continuity. We show that the impossibility result persists even without imposing the continuity axiom, and in...

A principal and an agent enter into a sequence of agreements. The principal faces an interim participation constraint at each date, but can commit to the current agreement; in contrast, the agent has the opportunity to renege on the current agreement. We study the time structure of agreement...

A concept of an egalitarian solution is developed within the framework of cooperative game theory. The solution is designed to capture the interplay between social values (in this case, egalitarianism) and individual behavior. Both the final outcomes possible coalitional deviations are...

We develop the measurement theory of polarization for the case in which income distributions can be described using density functions. The main theorem uniquely characterizes a class of polarization measures that fits into what we call the "identity-alienation" framework, and simultanously...

Suppose that the authors are interested in the distribution of a set of characteristics over a population. They study a precise sense in which this distribution can be said to be polarized and provide a theory of measurement. Polarization, as conceptualized here, is closely related to the...