Abstract
We define and study the concept of heavy viable trajectories of a controlled system with feedbacks in the framework a dynamical decentralized allocation mechanism in an exchange economy.
In this framework, the controls are the prices and the states of the system the consumptions of the consumers. Consumptions of each consumer evolve according a differential equation controlled by the price. Viable trajectories are the ones which obey the scarcity constraints : the sum of the consumptions must remain in the set of available commodities. Prices regulating viable trajectories evolve according a set-valued feedback map. Heavy viable trajectories are the ones associated to prices in the feedback map which evolve as slowly as possible : at each instant, the norm of the velocity of the price is minimal among the prices regulating a viable trajectory.
In this lecture, we construct the differential equation yielding heavy viable trajectories, providing a model of how the market may govern the evolution of prices. These results were obtained in collaboration with Halina Frankowska.
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Aubin, JP. (1984). Heavy viable trajectories of a decentralized allocation mechanism. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004975
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DOI: https://doi.org/10.1007/BFb0004975
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