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...

Outcomes of the shallow lake interest conflict are presented in a number of different contexts: quasi-static and dynamic social planning, and quasi-static one-shot and repeated non-cooperative play. As the underlying dynamics are non-convex, the analysis uses geometrical-numerical methods: the...

In this note we present as well necessary as sufficient conditions for existence of a Pareto optimum for general non-convex differential games. The obtained results are used to analyze the non-convex regular indefinite linear quadratic differential game. For the scalar case an algorithm is...

In this article we derive necessary and sufficient conditions for the existence of Pareto optimal solutions for an N player cooperative infinite horizon differential game. Firstly, we write the problem of finding Pareto candidates as solving N constrained optimal control subproblems. We derive...

In this note we reconsider Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption that every player can stabilize the system on his own. In...

Outcomes of the shallow lake interest conflict are presented in a number of different contexts: quasi-static and dynamic social planning, and quasi-static one-shot and repeated non-cooperative play. As the underlying dynamics are non-convex, the analysis uses geometrical-numerical methods: the...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has...

In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon. The performance function is assumed to be indefinite and the underlying system affine. We derive both necessary and sufficient conditions under which this game has a...

We analyze the problem of time-dependent channel coordination in the face of uncertain demand. The channel, composed of a manufacturer and a retailer, is to address a time-varying and uncertain price-dependent demand. The decision variables of the manufacturer are wholesale and (possibly zero)...

Almost every vendor faces uncertain and time-varying demand. Inventory level and price optimization while catering to stochastic demand are conventionally formulated as variants of newsvendor problem. Despite its ubiquity in potential applications, the time-dependent (multi-period) newsvendor...