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Algorithmic Principle of Least Revenue for Finding Market Equilibria

In: Optimization and Its Applications in Control and Data Sciences

Author

Listed:
  • Yurii Nesterov

    (Catholic University of Louvain (UCL))

  • Vladimir Shikhman

    (Catholic University of Louvain (UCL))

Abstract

In analogy to extremal principles in physics, we introduce the Principle of Least Revenue for treating market equilibria. It postulates that equilibrium prices minimize the total excessive revenue of market’s participants. As a consequence, the necessary optimality conditions describe the clearance of markets, i.e. at equilibrium prices supply meets demand. It is crucial for our approach that the potential function of total excessive revenue be convex. This facilitates structural and algorithmic analysis of market equilibria by using convex optimization techniques. In particular, results on existence, uniqueness, and efficiency of market equilibria follow easily. The market decentralization fits into our approach by the introduction of trades or auctions. For that, Duality Theory of convex optimization applies. The computability of market equilibria is ensured by applying quasi-monotone subgradient methods for minimizing nonsmooth convex objective—total excessive revenue of the market’s participants. We give an explicit implementable algorithm for finding market equilibria which corresponds to real-life activities of market’s participants.

Suggested Citation

  • Yurii Nesterov & Vladimir Shikhman, 2016. "Algorithmic Principle of Least Revenue for Finding Market Equilibria," Springer Optimization and Its Applications, in: Boris Goldengorin (ed.), Optimization and Its Applications in Control and Data Sciences, pages 381-435, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-42056-1_14
    DOI: 10.1007/978-3-319-42056-1_14
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