Contents lists available at ScienceDirect Journal of Economic Psychology journal homepage: www.elsevier.com/locate/joep Far but finite horizons promote cooperation in the Centipede game Eva M. Krockow ⁎ , Briony D. Pulford, Andrew M. Colman Department of Neuroscience, Psychology and Behaviour, University of Leicester, Leicester LE1 7RH, United Kingdom ARTICLE INFO JEL classification: C72 C92 D03 D74 Keywords: Centipede game Backward induction Endgame effect Cooperation Reciprocity PsycINFO classification: 2340 3020 ABSTRACT The sequential Centipede game models repeated reciprocal interaction, in which two players alternate in choosing between cooperation and defection. In an attempt to increase the game’s applicability to real-life decision contexts, we investigated the effects of game length and ter- mination rules on cooperation in the Centipede game. We found that increasing the game length from 8 to 20 decision nodes increased cooperation, but only if the game’s end was known to participants. Games with unknown ends manifested lower cooperation levels without an end- game effect (increased defection immediately before a known end). Random game termination by the computer appeared to increase the percentage of games adhering to the Nash equilibrium outcome mandated by game theory, and generally lowered cooperation levels. 1. Introduction Many human relationships are characterized by repeated interactions based on a reciprocal pattern of give-and-take. A familiar form is seen in dyadic relationships in which people take turns either cooperating by helping each other or defecting from the sequence of reciprocally helpful actions. In such situations, the benefit(b) of a cooperative action to the recipient is generally as great or greater than the cost (c) of the action to the cooperator, hence c ≤ b. Typical examples of this pattern include neighbors taking turns looking after each other’s pets while the other family is away, at a small cost in time and effort but large benefit to the recipients, and university researchers taking turns reading each other’s manuscripts or grant applications before submission, again at relatively small cost to the cooperator but potentially large benefit to the recipient. Against this background, Rosenthal’s (1981) Centipede game, a standard version of which is displayed in Fig. 1, can provide a helpful model. The original form of this sequential game includes two players with complete information (full knowledge of the game and the payoffs to both players) and perfect information (knowledge of all previous moves at every stage of the game) who take turns in deciding between two possible moves: a cooperative GO move that allows the game to continue, and a noncooperative or defecting STOP move that terminates the game immediately with a relatively favorable payoff to the defector. In Fig. 1, the numbered decision nodes are enclosed in circles for Player 1 and hexagons for Player 2. Player 1 begins at the left, choosing whether to GO (cooperate) or to STOP (defect), a STOP move terminating the game immediately with payoffs of 4 to Player 1 and 0 to Player 2 as shown in the terminal nodes at the bottom of the figure. A GO move hands the next move to Player 2, who can choose to STOP the game, with payoffs of 1 to Player 1 and 7 to Player 2, or can choose GO and hand Move 3 to Player 1, and so on. https://doi.org/10.1016/j.joep.2018.07.002 Received 23 September 2016; Received in revised form 12 January 2018; Accepted 5 July 2018 ⁎ Corresponding author. E-mail address: emk12@le.ac.uk (E.M. Krockow). Journal of Economic Psychology 67 (2018) 191–199 Available online 06 July 2018 0167-4870/ © 2018 Published by Elsevier B.V. T