We investigate the relations between different types of perfect equilibrium, introduced by Simon and Stinchcombe (1995) for games with compact action spaces and continuous payoffs. Simon and Stinchcombe distinguish two approaches to perfect equilibrium in this context, the classical "trembling hand" approach, and the so-called "finitistic" approach. We propose an improved definition of the finitistic approach, called global-limit-offinite perfection, and prove its existence.Despite the fact that the finitistic approach appeals to basic intuition, our results-specifically examples (1) and (2)-seem to imply a severe critique on this approach. In the first example any version of finitistic perfect equilibrium admits a Nash equilibrium strategy profile that is not limit admissible. The second example gives a completely mixed (and hence trembling hand perfect) Nash equilibrium that is not finitistically perfect.Further examples illustrate the relations between the two approaches to perfect equilibrium and the relation to admissibility and undominatedness of strategies.JEL Codes. C72.

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a b s t r a c tWe study a framework where two duopolists compete repeatedly in prices and where chosen prices potentially affect future market shares, but certainly do not affect current sales. This assumption of consumer inertia causes (noncooperative) coordination on high prices only to be possible as an equilibrium for low values of the discount factor. High discount factors increase opportunism and aggressiveness of competition to such an extent that high prices are no longer sustainable as an equilibrium outcome. Moreover, we find that both monopolization and enduring market share and price fluctuations (price wars) can be equilibrium path phenomena without requiring exogenous shocks in market or firm characteristics.

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