Inducible Games: Using Tit-for-Tat to Stabilize Outcomes

Brams, Steven J. and Kilgour, D. Marc (2012): Inducible Games: Using Tit-for-Tat to Stabilize Outcomes.

Abstract

Assume it is known that one player in a 2 x 2 game can detect the strategy choice of its opponent with some probability before play commences. We formulate conditions under which the detector can, by credibly committing to a strategy of probabilistic tit-for-tat (based on its imperfect detector), induce an outcome favorable to itself. A non-Nash, Pareto-optimal outcome is inducible—that is, it can be stabilized via probabilistic tit-for-tat—in 20 of the 57 distinct 2 x 2 strict ordinal games without a mutually best outcome (35 percent). Sometimes the inducement is “weak,” but more often it is “strong.” As a case study, we consider the current conflict between Israel and Iran over Iran’s possible development of nuclear weapons and show that Israel’s credible commitment to probabilistic tit-for-tat can, with sufficiently accurate intelligence, induce a cooperative choice by Iran in one but not the other of two plausible games that model this conflict.

• Item Type: MPRA Paper
• Language: English
• Keywords: 2 x 2 games; tit-for-tat; inducubility; Israel-Iran conflict; nuclear weapons
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D74 - Conflict ; Conflict Resolution ; Alliances ; Revolutions; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

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

Bergman, Ronen (2012). “Will Israel Attack Iran?” New York Times Magazine, January 30.

Biddle, W. F. (1972). Weapons, Technology, and Arms Control. New York: Praeger.

Biran, Dov, and Yair Tauman (2008). “The Role of Intelligence in Nuclear Deterrence.” Preprint, Department of Economics, Tel Aviv University.

Brams, Steven J. (1994). Theory of Moves. Cambridge: Cambridge University Press.

Brams, Steven J. (2011). Game Theory and the Humanities. New York: MIT Press.

Brams, Steven J., Morton D. Davis, and Philip D. Straffin Jr. (1979a). “The Geometry of the Arms Race.” International Studies Quarterly 23, no. 4 (December): 567-588.

Brams, Steven J., Morton D. Davis, and Philip D. Straffin Jr. (1979b). “A Reply to ‘Detection and Disarmament.’” International Studies Quarterly 23, no. 4 (December): 599-600.

Brams, Steven J., and D. Marc Kilgour (1988). Game Theory and National Security. Oxford, UK: Basil Blackwell.

Brams, Steven J., and D. Marc Kilgour (1992). “Putting the Other Side ‘On Notice’ Can Induce Compliance in Arms Control.” Journal of Conflict Resolution 36, no. 3 (September): 395-414.

Brams, Steven J., and D. Marc Kilgour (2009). “How Democracy Resolves Conflict in Difficult Games.” In Simon A. Levin (ed.), Games, Groups and the Global Good. Berlin: Springer, pp. 229-241.

Bronner, Ethan (2012). “Israelis Assess Threats by Iran as Partly Bluff.” New York Times, January 27.

Bruns, Bryan (2011). “Visualizing the Topology of 2 2 Games: From Prisoner’s Dilemma to Win-Win.” Paper presented at the International Conference on Game Theory, Stony Brook, NY, July 11-15.

Dacey, Raymond (1979). “Detection and Disarmament: A Comment on ‘The Geometry of the Arms Race.’” International Studies Quarterly 23, no. 4 (December): 589-598.

Erdbrink, Thomas (2012). “Iran Confirms Attack by Virus That Collects Information,” New York Times, May 29.

Lindgren, Bernard (1976). Statistical Theory, 3rd ed. New York: Macmillan.

Molander, Per (1985). “The Optimal Level of Generosity in a Selfish, Uncertain Environment.” Journal of Conflict Resolution 29, no. 4 (December): 511-518.

Nader, Aliteza (2012). “Influencing Iran’s Decisions on the Nuclear Program.” In Etel Solingen (ed.), Sanctions, Statecraft and Nuclear Proliferation. Cambridge: Cambridge University Press, 211-231.

Nowak, Martin A. (with Roger Highfield) (2011). SuperCooperators: Altruism, Evolution, and Why We Need Each Other to Succeed. New York: Free Press.

Nowak, Martin A. (2006). Evolutionary Dynamics: Exploring the Equations of Life. Cambridge, MA: Harvard University Press.

Robinson, David, and David Goforth (2005). The Topology of 2 2 Games. New York: Routledge.

Sigmund, Karl (2010). The Calculus of Selfishness. Princeton, NJ: Princeton University Press.

Solingen, Etel (2007). Nuclear Logics: Contrasting Paths in East Asia and the Middle East. Princeton, NJ: Princeton University Press.