An Interval Method for Seeking the Nash Equilibria of Non-cooperative Games

Kubica, Bartłomiej Jacek; Woźniak, A.

doi:10.1007/978-3-642-14403-5_47

Cited by 11 publications

(10 citation statements)

References 10 publications

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“…In (Kubica and Woźniak, 2010), we considered the necessary conditions of a Nash equilibrium and realized that -if no constraints are active -the point x has to satisfy the following conditions to be a Nash equilibrium:…”

Section: Necessary Conditions For a Snementioning

confidence: 99%

“…We use the following tools to solve it: -a variant of the monotonicity test -Algorithm 2; see also (Kubica and Woźniak, 2010), -a variant of the "concavity" test -Algorithm 4; e.g., (Kearfott, 1996),…”

Section: The Proposed Approachmentioning

confidence: 99%

“…In the first phase, we have a shared queue L -guarded by two mutexes, as described in (Kubica and Woźniak, 2010) -and several threads processing boxes in parallel.…”

Section: Parallelizationmentioning

confidence: 99%

“…The first three have been discussed in (Ślepowrońska, 1996) and then considered in Kołodziej et al, 2006;Kubica and Woźniak, 2010).…”

Section: Examples Of Games To Solvementioning

confidence: 99%

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Interval methods for computing strong Nash equilibria of continuous games

Kubica

Woźniak

2015

dmms

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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 with an approach to rigorously verify the existence of equilibria in certain points. A proper algorithm is presented. We formulate and prove propositions, that give us features which 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 also considered, and numerical results are presented. As a particular example, we consider the game of "misanthropic individuals", a game, invented by the first 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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Section: Necessary Conditions For a Snementioning

confidence: 99%

Section: The Proposed Approachmentioning

confidence: 99%

“…In the first phase, we have a shared queue L -guarded by two mutexes, as described in (Kubica and Woźniak, 2010) -and several threads processing boxes in parallel.…”

Section: Parallelizationmentioning

confidence: 99%

“…The first three have been discussed in (Ślepowrońska, 1996) and then considered in Kołodziej et al, 2006;Kubica and Woźniak, 2010).…”

Section: Examples Of Games To Solvementioning

confidence: 99%

See 2 more Smart Citations

Interval methods for computing strong Nash equilibria of continuous games

Kubica

Woźniak

2015

dmms

Self Cite

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show abstract

“…Seeking Nash equilibria in continuous games is a difficult problem [74]. Researchers in different fields, including mathematics, computer science, economics, and system engineering, have interest and need for techniques for finding Nash equilibria.…”

Section: Notes and Referencesmentioning

confidence: 99%