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4037. Heuristics and optimization-based methods for solving generalized Nash games: a comparison

Invited abstract in session TD-40: Tools and algorithms for equilibrium detection, stream Interfaces Between Optimization, Hierarchical Problems and Equilibrium Detection with Applications.

Tuesday, 14:30-16:00
Room: 96 (building: 306)

Authors (first author is the speaker)

1. Monica-Gabriela Cojocaru
Mathematics & Statistics, University of Guelph

Abstract

In this paper, we introduce three heuristic algorithms to investigate their in soilving Generalized Nash Equilibrium Problems (GNEP). The first is an evolutionary-inspired algorithm which utilizes competitive selection and (linear \& nonlinear) regression to motivate generations of new points. The second involves stochastic gradient descent of the Shadow Point function across mass numbers of agents to find game solutions. Last but not least, we present an ANN-based model with intelligent agents who solve a GNEP. These algorithms are evaluated on 2 and 3 player games in 2 and 3 dimensions, with both linear and non-linear shared constraints. The success of these algorithms is discussed and compared vis-a-vis existing, optimization-based methods (such as VI/QVI and KKT-based methods), and the limitations of the algorithms are explored. Finally, we introduce two measures of performance for all the algorithms in terms of their capability of finding and describing the entire solution set of a GNEP.

This is joint work with: Benjamin Benteke, Kira Tarasuk, Nick Hoover and Mihai Nica (at U of Guelph)

Keywords

Status: accepted

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