EURO 2024 Copenhagen
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1642. Robust Generalized Nash Equilibria

Invited abstract in session WC-43: Recent advances on Variational Inequalities and Equilibrium Problems II, stream Variational Inequalities and Equilibrium Problems: From Theoretical Advances to Real World Applications.

Wednesday, 12:30-14:00
Room: 99 (building: 306)

Authors (first author is the speaker)

1. Sara Mattia
Istituto di Analisi dei Sistemi ed Informatica, Consiglio Nazionale delle Ricerche
2. Mauro Passacantando
Department of Business and Law, University of Milano-Bicocca

Abstract

Robust optimization is an established technique for handling data uncertainty in optimization problems. However, most of the results refers to problems with a single decision maker, whereas less results are available for frameworks that include multiple decision makers. These settings are very common in several applied contexts, where different stakeholders may be involved in the decision making problem, with various roles and decision power. This is the case for example, for problems arising in healthcare, urban planning or shift scheduling problems. The present study aims at generalizing the results that are 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. Moreover, an existence result of robust equilibria is 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 provided.

Keywords

Status: accepted

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