A Note on Stabilizing Cooperation in the Centipede Game

Steven Brams () and D. Marc Kilgour
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D. Marc Kilgour: Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada

Games, 2020, vol. 11, issue 3, 1-7

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.

Keywords: centipede game; Prisoners’ Dilemma; subgame-perfect equilibrium; payoff exchange (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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