We bring together the theories of duality and dynamic programming. We show that the dual of a separable dynamic optimization problem can be recursively decomposed. We provide a dual version of the principle of optimality and give conditions under which the dual Bellman operator is a contraction...

Several recent papers have proposed recursive Lagrangian-based methods for solving dynamic contracting problems. These methods give rise to Bellman operators that incorporate either a dual inf-sup or a saddle point operation. We give conditions that ensure the Bellman operator implied by a dual...

Many dynamic incentive problems have primal recursive formulations in which utility promises serve as state variables. We associate families of dual recursive problems with these by selectively dualizing constraints. We make transparent the connections between recursive primal and dual...

Several recent papers have proposed recursive Lagrangian-basedmethods for solving dynamic contracting problems. Thesemethods give rise to Bellman operators that incorporate either a dual inf-sup or a saddle point operation. We give conditions that ensure the Bellman operator implied by a dual...

We analyse an overlapping generations model of voting on "reform projects". These resemble investments in that they first require some investment expenditure and later payoff. Since the time during which old people get the benefit is shorter, or because older people are more wealthy and hence...

In real-life elections, vote-counting is often imperfect. We analyze the consequences of such imperfections in plurality and runoff rule voting games. We call a strategy profile a robust equilibrium if it is an equilibrium if the probability of a miscount is positive but small. All robust...

We consider a model in which voters over time receive more information about their preferences concerning an irreversible social decision. Voters can either implement the project in the first period, or they can postpone the decision to the second period. We analyze the effects of different...

We bring together the theories of duality and dynamic programming. We show that the dual of an additively separable dynamic optimization problem can be recursively decomposed using summaries of past Lagrange multipliers as state variables. Analogous to the Bellman decomposition of the primal...

We also explore the robustness of our model when second period valuations are correlated across individuals, and when each individual's first and second period types are correlated.