Doing it Now, Later, or Never
21 Pages Posted: 18 Jul 2015
Date Written: July 7, 2015
Abstract
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, naïve 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.
Keywords: centipede games; subgame prefect ϵ-equilibria, time–inconsistent preferences, upper semi-continuous functions, sophisticated players, naive players
JEL Classification: C70, D11, D60, D74, D91
Suggested Citation: Suggested Citation