445. Robust Generalized Nash Equilibria
Invited abstract in session MC-10: Optimization, Learning, and Games II, stream Optimization, Learning, and Games.
Monday, 14:00-16:00Room: B100/8011
Authors (first author is the speaker)
| 1. | Mauro Passacantando
|
| Department of Business and Law, University of Milano-Bicocca | |
| 2. | Sara Mattia
|
| Istituto di Analisi dei Sistemi ed Informatica, Consiglio Nazionale delle Ricerche |
Abstract
Robust optimization is a well-established technique for dealing with data uncertainty in optimization problems. However, most results relate to single decision-maker problems, while fewer results are available for settings with multiple decision-makers. These settings are prevalent in several applied contexts, where different stakeholders may be involved in the decision problem, with different roles and decision power. This is the case, for example, in health care, urban planning, or shift scheduling problems. The present study aims at generalizing the results known for robust optimization problems with a single decision-maker to non-cooperative games where multiple decision-makers (players) are present. In particular, we focus on the Generalized Nash Equilibrium Problem (GNEP), where both the objective function and the feasible region of each player are affected by the actions of the other players. The robust version of a GNEP with uncertain parameters is defined, and its continuity, differentiability, convexity, and monotonicity properties are investigated. An existence result for robust equilibria is also given. In the case of linear or quadratic dependence of the objective functions and constraints on the uncertain parameters, equivalent reformulations of the robust GNEP are given.
Keywords
- Computational game theory
- Optimization under uncertainty
- Complementarity and variational problems
Status: accepted
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