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Mechanism design and allocation algorithms for network markets with piece-wise linear costs and externalities

Author

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  • Benjamin Heymann

    (Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems - CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique - Inria Saclay - Ile de France - Inria - Institut National de Recherche en Informatique et en Automatique)

  • Alejandro Jofré

    (CMM - Center for Mathematical Modeling - UCHILE - Universidad de Chile = University of Chile [Santiago])

Abstract

Motivated by market power in electricity market we introduce a mechanism design in [1] for simplified markets of two agents with linear production cost functions. In standard procurement auctions, the market power resulting from the quadratic transmission losses allow the producers to bid above their true value (i.e. production cost). The mechanism proposed in the previous paper reduces the producers margin to the society benefit. We extend those results to a more general market made of a finite number of agents with piecewise linear cost functions, which make the problem more difficult, but at the same time more realistic. We show that the methodology works for a large class of externalities. We also provide two algorithms to solve the principal allocation problem.

Suggested Citation

  • Benjamin Heymann & Alejandro Jofré, 2016. "Mechanism design and allocation algorithms for network markets with piece-wise linear costs and externalities," Working Papers hal-01416411, HAL.
    • Handle: RePEc:hal:wpaper:hal-01416411
    Note: View the original document on HAL open archive server: https://hal.science/hal-01416411
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    References listed on IDEAS

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    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. Juan Escobar & Alejandro Jofré, 2010. "Monopolistic competition in electricity networks with resistance losses," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 101-121, July.
    3. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
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    5. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701, October.
    6. Benjamin Heymann & Alejandro Jofré, 2016. "Mechanism Design and Auctions for Electricity Network," Working Papers hal-01315844, HAL.
    7. Xinmin Hu & Daniel Ralph, 2007. "Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices," Operations Research, INFORMS, vol. 55(5), pages 809-827, October.
    8. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190, October.
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