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Rockafellian relaxation and minimum-norm slack for the Walrasian equilibrium problem

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  • Julio Deride

Abstract

We propose a Rockafellian relaxation of the Walrasian equilibrium problem for an exchange economy that may not admit one. Market clearing is slackened by a non-negative variable $v$ whose norm is penalized; the relaxation is well posed throughout. As the penalty grows, the residual converges to a vector $v^*_\infty$ of minimum norm in the feasible range of excess demand, measuring the distance to the nearest equilibrium-admitting economy. A stressed Shapley--Shubik example recovers the analytical infeasibility floor to machine

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  • Julio Deride, 2026. "Rockafellian relaxation and minimum-norm slack for the Walrasian equilibrium problem," Papers 2607.04717, arXiv.org.
    • Handle: RePEc:arx:papers:2607.04717
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    References listed on IDEAS

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    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    2. Julio Deride & Alejandro Jofré & Roger J-B Wets, 2019. "Solving Deterministic and Stochastic Equilibrium Problems via Augmented Walrasian," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 315-342, January.
    3. Bergstrom Theodore C & Shimomura Ken-Ichi & Yamato Takehiko, 2009. "Simple Economies with Multiple Equilibria," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-31, December.
    4. Shapley, Lloyd S & Shubik, Martin, 1977. "An Example of a Trading Economy with Three Competitive Equilibria," Journal of Political Economy, University of Chicago Press, vol. 85(4), pages 873-875, August.
    5. Donald Brown & Felix Kubler, 2008. "Computational Aspects of General Equilibrium Theory," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-76591-2, December.
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