1997
DOI: 10.1006/game.1997.0531
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On the Maximal Number of Nash Equilibria in ann×nBimatrix Game

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Cited by 24 publications
(26 citation statements)
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“…For example, McKelvey and McLennan (1997) show that games with ten players with two strategies each, can have u p t o 1.3 million competely mixed (regular) equilibria. (See also Keiding (1997), McLennan (1997), and von Stengel (1999) for more literature on the maximal numbers of Nash equilibria of normal form games.) Although it needs to be checked exactly to what extent s u c h n umbers are related to say the number of Nash equivalence classes, it suggests that they could be large.…”
Section: Resultsmentioning
confidence: 99%
“…For example, McKelvey and McLennan (1997) show that games with ten players with two strategies each, can have u p t o 1.3 million competely mixed (regular) equilibria. (See also Keiding (1997), McLennan (1997), and von Stengel (1999) for more literature on the maximal numbers of Nash equilibria of normal form games.) Although it needs to be checked exactly to what extent s u c h n umbers are related to say the number of Nash equivalence classes, it suggests that they could be large.…”
Section: Resultsmentioning
confidence: 99%
“…For example, McKelvey and McLennan (1997) show that games with ten players with two strategies each, can have u p t o 1.3 million competely mixed (regular) equilibria. (See also Keiding (1997), McLennan (1997), and von Stengel (1999) for more literature on the maximal numbers of Nash equilibria of normal form games.) Although it needs to be checked exactly to what extent s u c h n umbers are related to say the number of Nash equivalence classes, it suggests that they could be large.…”
Section: Resultsmentioning
confidence: 99%
“…The Quint-Shubik conjecture follows for d ≤ 3 from the Upper Bound Theorem. This has been shown for d = 4 in [7] and [14]. The case d = 5 is open.…”
Section: Introductionmentioning
confidence: 82%
“…This implies the following bound on the number of equilibria [7]: For m = n, (n, 2n) grows asymptotically from n to n + 1 by an average factor of √ 27/4 = 2.598..., much faster than 2 n . We consider more precise asymptotics in Section 4.…”
Section: Cyclic Polytopes and A Lower Boundmentioning
confidence: 99%
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