Template-type: ReDif-Paper 1.0 Author-Name: Cingiz, K. Author-workplace-name: Microeconomics & Public Economics Author-Name: Flesch, J. Author-workplace-name: Quantitative Economics Author-Name: Herings, P.J.J. Author-workplace-name: Microeconomics & Public Economics Author-Name: Predtetchinski, A. Author-workplace-name: Microeconomics & Public Economics Title: Doing it now, later, or never 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. Series: GSBE Research Memoranda Creation-Date: 20150101 Number: 022 File-URL: https://cris.maastrichtuniversity.nl/ws/files/874367/guid-b870f657-e0de-4a99-9c11-01d8037931df-ASSET1.0.pdf File-Format: application/pdf File-Size: 488599 Handle: Repec:unm:umagsb:2015022 DOI: 10.26481/umagsb.2015022