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The Problem with Three: Great Power Competition Deterrence

  • Published
  • By Dr. Mel Deaile

Defining the relationship between two entities has provided some useful models. Marriage signifies the communal bond between two people. Newton helped define the gravitational relationship between two bodies. The Cold War brought insight into the working of strategic deterrence between two nuclear superpowers. When a third object is introduced into any of the above, the results are less predictable. A ‘love triangle’ brings disaster. The problem of three also affects physics and deterrence. The addition of another peer competitor challenges America’s strategic and nuclear deterrence posture.

America remains divided. Polarization will make it difficult, but not impossible, to formulate a bipartisan nuclear policy to address the country’s most urgent strategic challenge—competing with China and Russia. Under a new administration in the White House, the United States needs to deter not one but two rising regional powers. This era of great power competition does not mean a return to the days of the Cold War. Historical analogies and the application of bipolar deterrence theories will be in vain. While China has had nuclear weapons since 1964, its conventional and nuclear advances have brought it into direct competition with Russia and the United States.1 China recently announced its ability to field a true strategic triad comprised of land-based intercontinental ballistic missiles, sea-based ballistic missiles, and bombers capable of delivering nuclear weapons. A recent Department of Defense report to Congress examines the ascendency of China on the global stage.2 Twenty years ago, the US judged that China possessed a mostly archaic military. Today, the report assesses that China’s military is world-class. Conservative estimates indicated that China plans to grow its nuclear force in the coming decade to over 400 warheads.

The US, faced with the possibility of two pandemic relief acts, will need to start making fiscal decisions on the future of its national security. Nuclear programs will be part of that discussion. What model can policymakers draw upon to make tough decisions about the country’s nuclear force structure? When there were two players on the global stage, nuclear posture and policy decisions were made with respect to the capabilities of the main adversary. The addition of a third country into the calculation means the relationship between all parties becomes complicated. A deterrence theory that could model the many variables between the three states becomes highly complex, but classical physics and game theory might offer hope for a parsimonious approach to this three-country problem. History has shown the ability to describe universal constants between two bodies in either physics or international relations. Adding a third party to the existing system creates a complex dynamic few have solved.

Complications of Three International Players

Some have drawn on history, in particular the Cold War, to frame today’s strategic environment. Others have gone back even further to ancient Greece to find comparisons in the Peloponnesian war between Athens and Sparta to caution against falling into the Thucydides’ Trap, where an existing power finds itself at war with a rising power in order to protect its interests.3 While an easy comparison to the bipolar world, deterrence posturing differs today because of the multiple actors—US, Russia, and China—contending on the global stage. The Cold War demonstrated that deterrence theory proved successful when exercised between two nuclear superpowers. Today’s three-way power struggle brings a new problem to the fore. What is the best way to model the current strategic environment as well as nuclear deterrence in a multi-polar world?

Classical Physics and Modeling Relationships



The ‘three body problem’ demonstrated how a third entity complicates an existing model that correctly predicted two-body behavior. Locked in isolation during a pandemic, Sir Isaac Newton used his time in quarantine to finish work on calculus as well as expand his research on gravity.4 Newton’s universal gravitation described the relationship between two celestial bodies, where the gravity between two bodies is proportional to their mass and inversely proportional to the distance between them. Current decisions over the path forward on nuclear deterrence mirrors Newton’s discovery of the relationship between two entities. Cold War deterrence, largely focused on two countries, relied on strategic messaging, alerted nuclear missiles, and a secured second-strike capability to keep both sides treaty compliant. Actions by both sides were typically predicable and calculated. Newton, like the world today, struggled when a third party became part of the problem.5 His universal equation explained the relationship between the Sun and Earth. It explained the relationship between the Earth and a satellite as well as the satellite and the Sun. What Newton, and others after him, struggled with was explaining the relationship and interaction between all three at once. While the system remained stable, it was far from the calculated, predictable world Newton had previously modeled. This physics conundrum provided insight beyond its field; the three-body problem helped a classic military theorist perceive the true complexity of war.

Clausewitz, writing in the early 1800s, used early discussions on the three-body problem to help form his idea on the paradoxical trinity.6 The state, the people, and the Commander, according to Clausewitz, governed the conduct of war in states.7 The people provided the rage or hatred for the enemy, the state translated that irrational rage into rationale policy objectives, and the commander used his/her genius to overcome the friction in war to achieve those objectives. While each entity had its role, the relationship was more dynamic. Imagine three magnets of varying size with a pendulum suspended between them. Modeling the relationship between two magnets is possible but introduce a third magnet and the pendulum moves in an unpredictable pattern yet still maintains a position between the three entities. The same can be said for modern nuclear deterrence. Crafting a deterrent posture to address multiple countries at the same time cannot rely on applying the Cold War idea of simply applying assured destruction to two separate countries. In multiple player scenarios, the dynamic becomes more complicated.



Game theory provided several insights into nuclear deterrence through the Prisoner’s Dilemma, the duel, and even the game of chicken (brinksmanship). These modeled and predicted actions in two-player games. Like physics, the situation becomes more complicated when an additional player is introduced. The ‘truel,’ argued here, comes closest to modeling a three-player game, and it offers insights into multi-country nuclear deterrence. A ‘truel’ game is a three-way gunfight. The ending scene to The Good, The Bad, and the Ugly helps visualize this concept where there is a three-way standoff between Clint Eastwood, Lee Van Cleef, and Eli Wallach.8 In game theory, the ‘truel’ rules are a little less dramatic.9 The classic scenario is set-up between three armed players—Mr. Black, Mr. Grey, and Mr. White—who have increasing levels of accuracy with Mr. White being the most accurate (a sure shot). In accordance with the rules of the game, the players fire in ascending order of accuracy with Mr. Black, the worst shot (hitting only a third of his targets), going first. Game Theory suggests that Mr. Black, the first mover, will fire in the air passing his advantage to Mr. Gray. This will essentially make the situation a duel. Mr. Gray, a better shot, will eliminate the top competitor, Mr. White, leaving Mr. Black, the next in line to fire. With Mr. White eliminated (by Mr. Gray), Mr Black stands the best chance of winning the game even though he did not fire at any one when he had the opportunity.

The “truel” game can offer ideas into what kind of nuclear posture the US should adopt. The three-way gunfight would play out with the three ‘great powers’ assuming the roles of the players mentioned in the scenario above. Based on open-source reporting, it is known that China’s nuclear weapons are not as accurate as US nuclear weapons.10 China’s adaptation of a ‘no first use’ nuclear policy means its nuclear forces provide for retaliation in case of a nuclear attack. China anticipates using its inaccurate weapons and larger payloads in a countervalue role, targeting the population centers of any attacker. In the scenario above, China would be similar to Mr. Black. Avoiding first use, which would be similar to Mr. Black’s truel action of firing in the air, China has passed on firing and reduced the “truel” to a duel—yielding first mover advantage to one of the remaining two players. Those two remaining players are heavily armed. Although Russia and the US limit their strategic warheads to 1,550, Russia has greatly expanded its tactical nuclear capability (6000+) largely to offset America’s increasing conventional capability.

In the original “truel” game, the object of the game was to win by eliminating opponents. The goal in contemporary deterrence, however, is for all players to keep their weapons holstered. If China has passed on the ‘first shot,’ the US must posture itself to convince the other remaining player (Russia) to keep its weapon holstered. This means the US should have a nuclear force that is overtly responsive (a quick draw) as well as accurate. To keep its rapid response capability, the US should continue to modernize its fleet of intercontinental ballistic missiles, which have an unparalleled responsiveness and forces others to restrain from a pre-emptive strike. Submarine launched missiles act as a secured second strike in US deterrence and cannot approach the rapidity of an intercontinental ballistic missile response. This does not suggest that US forces are on a “hair-trigger alert,” but their rapid response capability will form the foundation of US nuclear deterrence going forward.11

What insights can the Newton/Clausewitz ‘three-body’ problem and the game theory ‘truel’ provide for the future of strategic deterrence and nuclear posture and policy? The three-body conundrum shows that interactions in a triune system are not always predictable, but the situation can be managed. The magnet moved unpredictably between components of the system but always stayed confined inside the model. In order to do this, the United States must constantly adjust inputs based on interactions within the system. For example, the United States used to have a continuous bomber presence on the island of Guam. It was a known fact that bombers would rotate through the island on a regular basis. In this era of Great Power Competition, Air Force Global Strike has shifted to a Bomber Task Force concept where bombers are sent as a show of assurance and deterrence to wherever a strategic message needs to be sent. Recently, those missions have been anywhere from the Artic to the Middle East.12 Going forward, static deterrence will not suffice. Deterrence will have to become agile and respond in the unpredictable, yet manageable, nature of this new three-way competition.



The ‘truel’ game helps illustrate actions the US must take with respect to its nuclear posture and policies. If strategic stability remains paramount in a Great Power Competition world, then continuing to increase accuracy, reducing yield, and adhering to ‘no first use’ must be a part of US nuclear policy. Accuracy goes hand-in-hand with first mover advantage and being the ‘fastest’ draw. The US is not just protecting itself in the ‘truel,’ but all the other nations under its umbrella. A counterforce, pre-emptive strike capability remains decisive to keeping other nations ‘fingers’ off the nuclear trigger. Furthermore, the United States must continue to modernize and increase its most responsive leg of the triad, the ICBM.

Cold War analogies do not correctly model the current international situation. Multi-body physics and multi-player games can offer insights into how the US should conduct strategic deterrence and structure its nuclear forces going forward.

Looking Ahead

As China’s economy and nuclear arsenal grows, the United States cannot simply rely on Cold War deterrence models for answers on how to posture its deterrence forces going forward. Traditionally, the US relied on its second-strike capability to maintain strategic stability. The game has changed. In a three-way scenario, the US must emphasize the precision and responsiveness in its nuclear posture. Coherent actions to couple these objectives are fielding accurate, low-yield warheads, and modernizing the most responsive leg of the triad, the ICBMs. Being the fastest and most accurate gunfighter forces others to keep their weapons holstered.

Dr. Mel Deaile

Dr. Mel Deaile is the Director of the School of Advanced Nuclear Deterrence Studies under the Air Command and Staff College at Air University, Maxwell AFB, AL. He is the author of Always At War, a book on organizational culture in SAC under General LeMay.


1 Office of the Secretary of Defense (OSD), Annual Report to Congress: Military and Security Developments Involving the People’s Republic of China 2020, (Washington, DC: OSD, 1 September 2020),

2 OSD, Annual Report to Congress.

3 Graham Allison, “Destined for War: America & Cina – Graham Allison – Talks at Google,” Talks at Google, uploaded 18 July 2017, YouTube video, 58:53,

4 James Gleick, Isaac Newton, (Vintage, 8 June 2004).

5 Stephen Wolfram, “Mechanisms in Programs and Nature,” in A New Kind of Science (Wolfram Media; 1st edition,14 May 2002), 972,

6 Christopher Bassford and Edward J. Villacres, “Reclaiming the Clausewitzian Trinity,” in Parameters, 1995,

7 Brian Cole, “Clausewitz’s Wondrous Yet Paradoxical Trinity: The Nature of War as a Complex Adaptive System,” Joint Force Quarterly 96, 1st Quarter, January 2020,

8 “The Good, the Bad and the Ugly (11/12) Movie CLIP - Three-Way Standoff (1966) HD,” Movieclips, uploaded 11 March 2015, YouTube video, 2:40,

9 Jay Bennett, “Riddle of the Week #11: The Truel: Difficulty level: Moderate,” Popular Mechanics, 12 January 2017,

10 David Logan, “The Dangerous Myths about China’s Nuclear Weapons,” War on the Rocks, 18 September 2020,

11 Mel Deaile and Al Mauroni, “The Need For Nuclear Alerts,” War on the Rocks, 6 May 2015,

12Air Force Global Strike Command AFSTRAT-AIR,

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