The search result changed since you submitted your search request. Documents might be displayed in a different sort order.
  • search hit 1 of 10
Back to Result List

Robust Market Equilibria under Uncertain Cost

Submission Status:under review
  • We consider equilibrium problems under uncertainty where firms maximize their profits in a robust way when selling their output. Robust optimization plays an increasingly important role when best guaranteed objective values are to be determined, independently of the specific distributional assumptions regarding uncertainty. In particular, solutions are to be determined that are feasible regardless of how the uncertainty manifests itself within some predefined uncertainty set. Our analysis adopts the robust optimization perspective in the context of equilibrium problems. First, we consider a singlestage, nonadjustable robust setting. We then go one step further and study the more complex two-stage or adjustable case where a part of the variables can adjust to the realization of the uncertainty. We compare equilibrium outcomes with the corresponding centralized robust optimization problem where the sum of all profits are maximized. As we find, the market equilibrium for the perfectly competitive firms differs from the solution of the robust central planner, which is in stark contrast to classical results regarding the efficiency of market equilibria with perfectly competitive firms. For the different scenarios considered, we furthermore are able to determine the resulting price of anarchy. In the case of non-adjustable robustness, for fixed demand in every time step the price of anarchy is bounded whereas it is unbounded if the buyers are modeled by elastic demand functions. For the two-stage adjustable setting, we show how to compute subsidies for the firms that lead to robust welfare optimal equilibria.

Download full text files

Export metadata

Author:Christian Biefel, Frauke Liers, Jan Rolfes, Lars Schewe, Gregor Zöttl
Document Type:Preprint
Date of Publication (online):2021/08/25
Date of first Publication:2021/08/25
Release Date:2021/08/25
Tag:Adjustable Robustness; Continuous Optimization; Equilibrium Problems; Robust Optimization
Page Number:24
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
University of Edinburgh
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International