A note on stabilizing cooperation in the centipede game

Steven J. Brams, D. Marc Kilgour

    Research output: Contribution to journalArticlepeer-review

    Abstract

    In the much-studied Centipede Game, which resembles the 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 Nash equilibrium in the transformed Centipede Game, called the Reciprocity Game, is unique—unlike the Centipede Game, wherein there are several 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.

    Original languageEnglish (US)
    Article number35
    Pages (from-to)1-7
    Number of pages7
    JournalGames
    Volume11
    Issue number3
    DOIs
    StatePublished - Sep 2020

    Keywords

    • Centipede game
    • Payoff exchange
    • Prisoners’ Dilemma
    • Subgame-perfect equilibrium

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty
    • Applied Mathematics

    Fingerprint Dive into the research topics of 'A note on stabilizing cooperation in the centipede game'. Together they form a unique fingerprint.

    Cite this