Biefel C, Liers F, Rolfes J, Schewe L, Zöttl G (2022)
Publication Status: Accepted
Publication Type: Journal article
Future Publication Type: Journal article
Publication year: 2022
Book Volume: 302
Pages Range: 1230-1241
Journal Issue: 3
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 deter-mined that are feasible regardless of how the uncertainty manifests itself within some predefined uncertainty set. Our analysis adopts the robust optimizationperspective in the context of equilibrium problems. First, we consider a single-stage, 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 canadjust to the realization of the uncertainty. We compare equilibrium outcomes with the corresponding centralized robust optimization problem where thesum of all profits are maximized. As we find, the market equilibrium forthe perfectly competitive firms differs from the solution of the robust central planner, which is in stark contrast to classical results regarding the efficiency ofmarket 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.
Biefel, C., Liers, F., Rolfes, J., Schewe, L., & Zöttl, G. (2022). Robust Market Equilibria under Uncertain Cost. European Journal of Operational Research, 302(3), 1230-1241. https://dx.doi.org/10.1016/j.ejor.2022.02.030
Biefel, Christian, et al. "Robust Market Equilibria under Uncertain Cost." European Journal of Operational Research 302.3 (2022): 1230-1241.