Interval methods for computing strong Nash equilibria of continuous games

Authors

  • Bartłomiej Kubica Warsaw University of Technology
  • Adam Woźniak Warsaw University of Technology

DOI:

https://doi.org/10.7494/dmms.2015.9.1.63

Keywords:

strong Nash equilibria, continuous games, interval computations, numerical game solving

Abstract

The problem of seeking strong Nash equilibria of a continuous game is considered. For some games these points cannot be found analytically, only numerically. Interval methods provide us an approach to rigorously verify the existence of equilibria in certain points. A proper algorithm is presented. We formulate and prove propositions, giving us features that have to be used by the algorithm (to the best knowledge of the authors, these propositions and properties are original). Parallelization of the algorithm is considered, also, and numerical results are presented. As a particular example, we consider the game of "misanthropic individuals", a game (invented by the frst author) that may have several strong Nash equilibria, depending on the number of players. Our algorithm is able to localize and verify these equilibria.

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Published

2016-02-17

How to Cite

Kubica, B., & Woźniak, A. (2016). Interval methods for computing strong Nash equilibria of continuous games. Decision Making in Manufacturing and Services, 9(1), 63–78. https://doi.org/10.7494/dmms.2015.9.1.63
Received 2015-07-15
Accepted 2015-07-15
Published 2016-02-17