A Note on Stabilizing Cooperation in the Centipede Game

Steven Brams () and Marc Kilgour

MPRA Paper from University Library of Munich, Germany

Abstract: In the much-studied Centipede Game, which resembles Iterated Prisoners’ Dilemma, two players successively choose between (1) cooperating, by continuing play, or (2) defecting and terminating play. The subgame-perfect Nash equilibrium implies that play terminates on the first move, even though continuing play can benefit both players—but not if the rival defects immediately, which it has an incentive to do. We show that, without changing the structure of the game, interchanging the payoffs of the two players provides each with an incentive to cooperate whenever its turn comes up. The unique Nash equilibrium in the transformed Centipede Game, called the Reciprocity Game, is unique—unlike the Centipede Game, where there are many Nash equilibria. The Reciprocity Game can be implemented noncooperatively by adding, at the start of the Centipede Game, a move to exchange payoffs, which it is rational for the players to choose. What this interchange signifies, and its application to transforming an arms race into an arms-control treaty, are discussed.

Keywords: Centipede Game; Prisoners’ Dilemma; Subgame-Perfect Equilibrium; Payoff Exchange (search for similar items in EconPapers)
JEL-codes: C7 C72 D63 (search for similar items in EconPapers)
Date: 2021-03
New Economics Papers: this item is included in nep-gth, nep-mic and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in Games 35.11(2020): pp. 1-7

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/106809/1/MPRA_paper_106809.pdf original version (application/pdf)

Related works:
Journal Article: A Note on Stabilizing Cooperation in the Centipede Game (2020)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:106809

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().