A Note on Stabilizing Cooperation in the Centipede Game

Brams, Steven and Kilgour, Marc (2021): A Note on Stabilizing Cooperation in the Centipede Game. Published in: Games , Vol. 11, No. 35 (20 August 2020): pp. 1-7.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Centipede Game; Prisoners’ Dilemma; Subgame-Perfect Equilibrium; Payoff Exchange
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

References

Axelrod, Robert (1984). The Evolution of Cooperation. New York: Basic Books.

García-Pola, Bernado, Nagore Irberri, and Jaromír Kovárí. “Non-Equilibrium Play in Centipede Games.” Preprint. https://economics.stanford.edu/sites/g/files/sbiybj9386

Lebow, Richard Ned, and Janice Gross Stein (1987). “Beyond Deterrence.” Journal of Social Issues 43, no. 4 (Winter): 5-71.

Levitt, Steven D, John A. List, and Sally E. Sadoff (2011). “Checkmate: Exploring Backward Induction among Chess Players.” American Economic Review 101, no. 2 (April): 975-990.

McKelvey, Richard, and Thomas Palfrey (1992). “An Experimental Study of the Centipede Game.” Econometrica 60, no. 4 (July): 803-836.

Nagel, Rosemarie, and Fang Fang Tang (1998). “Experimental Results on the Centipede Game in Normal Form: An Investigation on Learning.” Journal of Mathematical Psychology 42, nos. 2-3 (June): 356-384.

Palacio-Huerta, Ignacio, and Oscar Volij (2009). “Field Centipedes.” American Economic Review 99, no. 4 (September): 1619-1635.

Press, William H., and Freeman J. Dyson (2012). “Iterated Prisoner’s Dilemma Contains Strategies that Dominate an Evolutionary Opponent.” PNAS 109, no. 26 (June 26): 10409-10413.

Rosenthal, Robert W. (1981). “Games of Perfect Information; Predatory Pricing and the Chain-Store Paradox.” Journal of Economic Theory 23, no. 1 (August): 92-100.