1997
DOI: 10.1016/s0165-4896(97)00002-4
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On the invariance of solutions of finite games

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Cited by 9 publications
(11 citation statements)
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“…While perfect equilibrium satisfies invariance in the setting of finite strategic form games-see for example Mertens (2003) and Vermeulen and Jansen (1997)-perfection violates invariance even in games with complete information if the action spaces are infinite, as is pointed out in Bajoori et al (2013).…”
Section: Ordinalitymentioning
confidence: 96%
“…While perfect equilibrium satisfies invariance in the setting of finite strategic form games-see for example Mertens (2003) and Vermeulen and Jansen (1997)-perfection violates invariance even in games with complete information if the action spaces are infinite, as is pointed out in Bajoori et al (2013).…”
Section: Ordinalitymentioning
confidence: 96%
“…This is surprising in the sense that ∞ is payoff equivalent to 1 for player 2. Thus, both strong and weak perfection violate invariance in this setting, while perfect equilibrium satisfies invariance in the setting of finite strategic form games (see for example Mertens [18] and Vermeulen and Jansen [25]). …”
Section: Invariancementioning
confidence: 99%
“…Now let (Γ * ) be the game with the same strategy space as Γ for which the payoff function of a player equals the composition of the payoff function of that player in the game Γ and f . Since each f i preserves best replies (by Lemma 1 of (Vermeulen and Jansen, 1997)), the games (Γ * ) and Γ are abr-equivalent. Since, moreover, f is a reduction map from (Γ * ) to Γ * , f −1 (S) is a BR-set of the game (Γ * ) .…”
Section: Theorem 2 the Solution τ Is Abr-invariantmentioning
confidence: 99%
“…Let Γ and Γ * be two abr-equivalent games and let S be a solution set of the game Γ * . Then, by Theorem 3 of (Vermeulen and Jansen, 1997), it must be a closed and connected set of perfect equilibria of the game Γ . In order to show that S is also an extensible set of the game Γ , take a reduction map f from a game Γ to Γ .…”
Section: Theorem 2 the Solution τ Is Abr-invariantmentioning
confidence: 99%