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Projected dynamical systems modeling and computation of spatial network equilibria
Author(s) -
Nagurney Anna,
Takayama Takashi,
Zhang Ding
Publication year - 1995
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230260203
Subject(s) - computation , computer science , set (abstract data type) , walrasian auction , convergence (economics) , mathematical optimization , variational inequality , commodity , projected dynamical system , dynamical systems theory , algorithm , mathematics , common value auction , economics , linear dynamical system , quantum mechanics , programming language , economic growth , generalized second price auction , market economy , statistics , physics , random dynamical system , auction theory
In this paper, we consider the price formulation—rather than the quantity formulation—of spatial network equilibria and introduce a projected dynamical system, whose set of stationary points corresponds to the set of solutions of the governing variational inequality problem. We then interpret the dynamical system as a tatonnement process in which the commodity prices and shipments are updated simultaneously. We propose an Euler‐type method for the computation of the commodity prices and trade patterns, provide convergence results, and demonstrate that the algorithm can be implemented on massively parallel architectures. The notable feature of the algorithm is that the prices and shipments can be computed independently and in closed form. Finally, we illustrate the performance of the implemented algorithm on the Thinking Machine's CM‐2 and CM‐5 architectures.