Cake Eating, Exhaustible Resource Extraction, Life-cycle Saving, and Non-atomic Games: Existence Theorems for a Class of Optimal Allocation Problems
نویسنده
چکیده
This paper investigates the problem concerning the existence of a solution to a diverse class of optimal allocation problems which include models of cake eating, exhaustible resource extraction, life-cycle saving, and nonatomic games. A new formulation that encompasses all these diverse models is provided. Examples of these models for which a solution does not exist and the causes of the non-existence are studied. Two theorems are provided to tackle the existence problem under di¤erent conditions. Several analytical examples with a closed-form solution are o¤ered to illustrate the usefulness of the existence theorems. Keywords: cake eating, exhaustible resource extraction, life-cycle saving, non-atomic games, optimal allocation, existence Journal of Economic Literature Classi cation: C61, C71, D11, D91, E21, Q32 I thank Sergey Aseev, James Davies, Gustav Feichtinger, and Peter Kort for helpful discussions. I have bene ted from presenting a preliminary version of the paper in the Ninth Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamic at the University of Montreal in May 2007. Wung Lik Ng and Peter Tsui provided research assistance. This research was supported by Hong Kong Research Grants Council CERG HKUST6476/05H.
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