Strong Nash equilibria and mixed strategies

Eleonora Braggion (), Nicola Gatti (), Roberto Lucchetti (), Tuomas Sandholm () and Bernhard von Stengel
Additional contact information
Eleonora Braggion: Politecnico di Milano
Nicola Gatti: Politecnico di Milano
Roberto Lucchetti: Politecnico di Milano
Tuomas Sandholm: Carnegie Mellon University

International Journal of Game Theory, 2020, vol. 49, issue 3, No 3, 699-710

Abstract: Abstract We study strong Nash equilibria in mixed strategies in finite games. A Nash equilibrium is strong if no coalition of players can jointly deviate so that all players in the coalition get strictly better payoffs. Our main result concerns games with two players and states that if a game admits a strong Nash equilibrium, then the payoff pairs in the support of the equilibrium lie on a straight line in the players’ utility space. As a consequence, the set of games that have a strong Nash equilibrium in which at least one player plays a mixed strategy has measure zero. We show that the same property holds for games with more than two players, already when no coalition of two players can profitably deviate. Furthermore, we show that, in contrast to games with two players, in a strong Nash equilibrium an outcome that is strictly Pareto dominated may occur with positive probability.

Keywords: Noncooperative games; Strong Nash equilibrium; Mixed strategies; Pareto efficiency (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s00182-020-00723-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:49:y:2020:i:3:d:10.1007_s00182-020-00723-3

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2

DOI: 10.1007/s00182-020-00723-3

Access Statistics for this article

International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel

More articles in International Journal of Game Theory from Springer, Game Theory Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().