Solving Maxmin Optimization Problems via Population Games

39 Pages Posted: 15 Nov 2022 Last revised: 21 Feb 2024

See all articles by Anne Balter

Anne Balter

Tilburg University; Netspar

Johannes M. Schumacher

University of Amsterdam - Department of Quantitative Economics (KE)

Nikolaus Schweizer

Tilburg School of Economics and Management

Date Written: February 21, 2024

Abstract

Population games are games with a finite set of available strategies and an infinite number of players, in which the reward for choosing a given strategy is a function of the distribution of players over strategies. The paper shows that, in a certain class of maxmin optimization problems, it is possible to associate a population game to a given maxmin problem in such a way that solutions to the optimization problem are found from Nash equilibria of the associated game. Iterative solution methods for maxmin optimization problems can then be derived from systems of differential equations whose trajectories are known to converge to Nash equilibria. In particular, we use a discrete-time version of the celebrated replicator equation of evolutionary game theory, also known in machine learning as the exponential multiplicative weights algorithm. The resulting algorithm can be viewed as a generalization of the Iteratively Reweighted Least Squares (IRLS) method, which is well known in numerical analysis as a useful technique for solving Chebyshev function approximation problems on a finite grid. Examples are provided to show the use of the generalized IRLS method in collective investment and in decision making under model uncertainty.

Keywords: Maxmin, multicriteria optimization, collective decision, population games, Nash equilibrium.

JEL Classification: C61, C73, D70, D81, G11

Suggested Citation

Balter, Anne and Schumacher, J.M. (Hans) and Schweizer, Nikolaus, Solving Maxmin Optimization Problems via Population Games (February 21, 2024). Available at SSRN: https://ssrn.com/abstract=4264811 or http://dx.doi.org/10.2139/ssrn.4264811

Anne Balter

Tilburg University ( email )

P.O. Box 90153
Tilburg, DC Noord-Brabant 5000 LE
Netherlands

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

J.M. (Hans) Schumacher (Contact Author)

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Nikolaus Schweizer

Tilburg School of Economics and Management ( email )

PO Box 90153
Tilburg, 5000 LE Ti
Netherlands

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