Two Against One: Deterrence in the Triad
-
Frank C. Zagare
Abstract
This essay explores a deterrence relationship between one defender and two challengers that are interconnected game-theoretically but are otherwise acting independently. In the double deterrence game model, the primary challenger makes the first move, defender, the second, and the secondary challenger makes its move only after the defender and the primary challenger have made their choices. In other words, the threat of the secondary challenger is both latent and contingent. There are four types of defenders, and three types of the two challengers. These preference assumptions define 36 distinct strategic environments, or games. These games are analyzed under both complete and incomplete information. The results are highly sensitive to the specific combination of player types. Deterrence is most likely to succeed when a defender’s threat is highly credible, and to fail when it is low. The secondary challenger is most likely to have an impact on play only at intermediate levels of the defender’s and the primary challenger’s credibility. Assuming a rising challenger, or a declining defender, or both, a danger zone will exist just prior to, or immediately after, the primary challenger has achieved parity with the defender, that is, when a balance of capabilities exists. The principal aim of a defender of the status quo facing two challengers acting independently should be on preventing a challenge by its primary opponent. This conclusion is robust no matter what configuration of player types one assumes.
Appendix
List of possible outcomes.
| Outcome |
|---|
| a. Status Quo |
| b. Challenger 1 Wins |
| c. Defender Wins |
| d. Challengers 1 and 2 Win |
| e. Conflict with Challenger 2 (Challenger 1 Wins) |
| f. Conflict with Challenger 1 |
| g. Conflict with Challengers 1 and 2 |
Restrictions on preferences.
| Types of players | Restrictions on preferences |
|---|---|
| All types of defender: | a ≻ c; b ≻ (d, e); f ≻ g |
| Staunch | (f, g) ≻ (b, d, e); e ≻ d |
| Semi- Staunch | (f, g) ≻ (b, d, e); d ≻ e |
| Submissive | (b, d, e) ≻ (f, g); d ≻ e |
| Semi- Submissive | (b, d, e) ≻ (f, g); e ≻ d |
| All types of Challenger 1: | b ∼ d ∼ e ≻ a ≻ (c, f, g) |
| Hesitant | c ≻ f ∼ g |
| Determined | f ∼ g ≻ c |
| Cautious | g ≻ c ≻ f |
| All types of Challenger 2: | d ≻ (b, e, f, g) |
| Persistent | e ≻ b |
| Restrained | b ≻ e |
| Reluctant | f ≻ g |
| Opportunistic | g ≻ f |
References
Altfeld, Michael F., and Bruce Bueno de Mesquita. 1979. “Choosing Sides in Wars.” International Studies Quarterly 23: 87–112. https://doi.org/10.2307/2600275.Search in Google Scholar
Brodie, Bernard. 1959. “The Anatomy of Deterrence.” World Politics 11: 173–9. https://doi.org/10.2307/2009527.Search in Google Scholar
Intriligator, Michael D., and Dagobert L. Brito. 1984. “Can Arms Races Lead to the Outbreak of War?” Journal of Conflict Resolution 28: 63–84. https://doi.org/10.1177/0022002784028001004.Search in Google Scholar
Iwanami, Yukari. 2023. “Asymmetric Burden-sharing and the Restraining and Deterrence Effects of Alliances.” Journal of Peace Research. https://doi.org/10.1177/00223433231158146.Search in Google Scholar
Krainin, Colin, and Thomas Wiseman. 2016. “War and Stability in Dynamic International Systems.” The Journal of Politics 78: 1139–52. https://doi.org/10.1086/686307.Search in Google Scholar
Lakatos, Imre. 1970. “Falsification and the Methodology of Scientific Research Programs.” In Criticism and the Growth of Knowledge, edited by Imre Lakatos, and Alan Musgrave. Cambridge: Cambridge University Press.Search in Google Scholar
Mearsheimer, John J. 1983. “The Case for a Ukrainian Nuclear Deterrent.” Foreign Affairs 72: 50–66. https://doi.org/10.2307/20045622.Search in Google Scholar
Organski, A.F.K., and Jacek Kugler. 1980. The War Ledger. Chicago: University of Chicago Press.10.7208/chicago/9780226351841.001.0001Search in Google Scholar
Overy, Richard. 2021. Blood and Ruins: The Last Imperial War, 1931 – 1945. New York: Penguin Books.Search in Google Scholar
Powell, Robert. 2017. “Taking Sides in Wars of Attrition.” American Political Science Review 111: 219–36. https://doi.org/10.1017/s0003055416000782.Search in Google Scholar
Quackenbush, Stephen L. 2006. “Not Only Whether but Whom: Three-Party Extended Deterrence.” Journal of Conflict Resolution 50: 562–83. https://doi.org/10.1177/0022002706290431.Search in Google Scholar
Quackenbush, Stephen L. 2010. “General Deterrence and International Conflict: Testing Perfect Deterrence Theory.” International Interactions 36: 60–85. https://doi.org/10.1080/03050620903554069.Search in Google Scholar
Quackenbush, Stephen L. 2011. Understanding General Deterrence: Theory and Application. New York: Palgrave Macmillan.10.1057/9780230370791Search in Google Scholar
Rasmusen, Eric. 1989. Games and Information: An Introduction to Game Theory, 2nd ed. Cambridge: Blackwell.Search in Google Scholar
Schelling, Thomas C. 1966. Arms and Influence. New Haven: Yale University Press.Search in Google Scholar
Schweller, Randall. 1998. Deadly Imbalances: Tripolarity and Hitler’s Strategy of World Conquest. New York: Columbia University Press.Search in Google Scholar
Selten, Reinhard. 1975. “A Re-examination of the Perfectness Concept for Equilibrium Points in Extensive Games.” International Journal of Game Theory 4: 25–55. https://doi.org/10.1007/bf01766400.Search in Google Scholar
Snyder, Glenn H., and Paul Diesing. 1977. Conflict Among Nations: Bargaining, Decision Making and System Structure in International Crises. Princeton: Princeton University Press.Search in Google Scholar
Waltz, Kenneth N. 2012. “Why Iran Should Get the Bomb: Nuclear Balancing Would Mean Stability.” Foreign Affairs 91: 2–5.Search in Google Scholar
Zagare, Frank C. 1996. “Classical Deterrence Theory: A Critical Assessment.” International Interactions 21: 365–87. https://doi.org/10.1080/03050629608434873.Search in Google Scholar
Zagare, Frank C. 2019. Game Theory, Diplomatic History and Security Studies. Oxford: Oxford University Press.10.1093/oso/9780198831587.001.0001Search in Google Scholar
Zagare, Frank C., and D. Marc Kilgour. 2000. Perfect Deterrence. Cambridge: Cambridge University Press.10.1017/CBO9780511491788Search in Google Scholar
Zagare, Frank C., and D. Marc Kilgour. 2003. “Alignment Patterns, Crisis Bargaining, and Extended Deterrence: A Game-Theoretic Analysis.” International Studies Quarterly 47: 587–615. https://doi.org/10.1046/j.0020-8833.2003.00280.x.Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Research Articles
- Two Against One: Deterrence in the Triad
- Rationality of the Terrorist Group and Government’s Policy: A Game Theoretic Approach
- Does Militarization Hinder Female Labor Income Share?
- Analyzing the Tripartite Relationship Among Public Debt, Economic Growth, and Political Risks: A Panel VAR Approach
- Armed Conflicts and Household Socioeconomic Status in the Lake Chad Basin: A Random Coefficient Model Approach
Articles in the same Issue
- Frontmatter
- Research Articles
- Two Against One: Deterrence in the Triad
- Rationality of the Terrorist Group and Government’s Policy: A Game Theoretic Approach
- Does Militarization Hinder Female Labor Income Share?
- Analyzing the Tripartite Relationship Among Public Debt, Economic Growth, and Political Risks: A Panel VAR Approach
- Armed Conflicts and Household Socioeconomic Status in the Lake Chad Basin: A Random Coefficient Model Approach
