On the Maximal Number of Nash Equilibria in ann×nBimatrix Game

Keiding, Hans

doi:10.1006/game.1997.0531

“…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%

On some geometry and equivalence classes of normal form games

Germano

¹

2006

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Equivalence classes of normal form games are de ned using the geometry of correspondences of standard equilibrium concepts like correlated, Nash, and robust equilibrium, or risk dominance and rationalizability. Resulting equivalence classes are fully characterized and compared across di erent equilibrium concepts for 2 2 games. It is argued that the procedure can lead to broad and gametheoretically meaningful distinctions of games as well as to alternative w ays of viewing and testing equilibrium concepts. Larger games are also brie y considered. Keywords Non-cooperative games, classi cation and equivalence classes, experimental games, geometry of games. JEL Classi cation C 7 0 , C 7 2 , C 7 8 , C 9 0 , C 9 1 .

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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%

On Some Geometry and Equivalence Classes of Normal Form Games

Germano

¹

2003

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Equivalence classes of normal form games are de ned using the geometry of correspondences of standard equilibrium concepts like correlated, Nash, and robust equilibrium, or risk dominance and rationalizability. Resulting equivalence classes are fully characterized and compared across di erent equilibrium concepts for 2 2 games. It is argued that the procedure can lead to broad and gametheoretically meaningful distinctions of games as well as to alternative w ays of viewing and testing equilibrium concepts. Larger games are also brie y considered. Keywords Non-cooperative games, classi cation and equivalence classes, experimental games, geometry of games. JEL Classi cation C 7 0 , C 7 2 , C 7 8 , C 9 0 , C 9 1 .

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“…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%