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Doing it now, later, or never

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Article
Author/s: 
Kutay Cingiz, János Flesch, P. Jean-Jacques Herings, Arkadi Predtetchinski
Games and Economic Behavior
Issue number: 
Volume 97, May 2016
Publisher: 
Elsevier
Year: 
2016
Journal pages: 
174-185
We study centipede games played by an infinite sequence of players. Following the literature on time-inconsistent preferences, we distinguish two types of decision makers, naive and sophisticated, and the corresponding solution concepts, naive ϵ-equilibrium and sophisticated ϵ-equilibrium. We show the existence of both naive and sophisticated ϵ-equilibria for each positive ϵ. Under the assumption that the payoff functions are upper semicontinuous, we furthermore show that there exist both naive and sophisticated 0-equilibria in pure strategies. We also compare the probability to stop of a naive versus a sophisticated decision maker and show that a sophisticated decision maker stops earlier.
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