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Prisoners of Power - Analysing the US-China Patch-Up Through Game Theory

Game theory deals with interdependent situations and rational actors and how they make choices, understanding the subsequent consequences. This method has long been applied to analyse, understand, and predict the course of actions of different state actors in various geopolitical scenarios. Here, we will try to look at the recent patch-up between the US and China in the Biden-Xi meeting through one of the games in game theory.

An Illustration on Prisoners of Power

Illustration by The Geostrata

The Prisoner’s Dilemma is a concept that shows how two participants who are trapped in a particular situation and are unable to coordinate their real intentions with each other might react based on choices and possible outcomes.

The dilemma focuses on self-interest vs. mutual benefits and how rational participants may react depending on cost-benefit analysis.


  1. Cooperate - Cooperate (C-C) If both parties choose to show restraint and not betray each other, then they will both have moderate losses. Thus, mutual cooperation will lead to mutual but limited benefit.

  2. Betray - Betray (B-B) If both participants decide to betray each other, they will both incur heavy losses. Mutual betrayal will lead to mutually assured destruction.

  3. Cooperate or Betray (C-B) or (B-C) If any one of the parties decides to betray while the other party chooses to cooperate, then the betraying party will have maximum benefits and the cooperating side will face heavy losses. This scenario shows the conflict between self-interest and mutual trust. How the possibility of more gains could drive states to confront or betray other states instead of cooperating with them.

Here, betrayal is inferred as any action taken against the interest of the second party; this includes, but is not limited to, pressuring and direct and indirect confrontation.

Whereas, cooperation means any action taken with consideration and preservation of another party’s interests along with self-interest. It also consists of aligning common goals and working together to achieve them.


  1. Zero-Sum Game: In this situation, the gain of one party is balanced by the loss of another. So there is no net change; it is always zero. A prisoner’s dilemma cannot be a zero-sum game, as mutual cooperation can lead to mutual benefits.

  2. Positive-sum game: This scenario talks about the increase in total benefits for both players when they cooperate.

  3. Negative-sum game: Total benefits decrease when both players betray each other and both incur heavy losses. 

  4. Mixed-Strategy Game: In this scenario, players change their choices from time to time based on different probabilities. Thus, they can cooperate for some time and betray each other occasionally. This scenario has an element of unpredictability in it.


The US and PRC are two very different nations; one is a democratic nation with changing leadership, policies, and public opinions, while the second is an autocratic nation where one party and now one leader dictates everything. Yet both the US and PRC can be assumed to be equally rational players, for both understand the threat and value of their confrontation and cooperation, respectively.


Over the last eight years, tensions between the two nations have been rising continuously. When Trump took office in 2016, both nations engaged in trade and tariff wars, and even when Biden came into power, though the anti-China rhetoric slowed down, but the pressure continued to rise. Trade wars were replaced by sanctions on technology and AI, among other issues. 

On the other side, fentanyl flow from China has wreaked havoc in the US, killing more than 100,000 people in 2022 due to overdose. The Spy Balloon incident deepened the distrust between China and the US, leading China to close communication with the US, especially in military terms.

This breakup between these two powers happened at a time when the world has been engulfed in bloody conflicts, climate crises, and economic uncertainty. The Russia-Ukraine conflict and the recent Israel-Hamas war have divided the world, putting the US and China on opposite sides. Yet issues like climate change and economic interdependence still require these two countries to cooperate.

In light of this background, we can now look at how different choices that could have been made by these two nations before the Biden-Xi meeting could have resulted in different outcomes.



In this scenario, we would have to assume the US is a party that is willing to cooperate because it was the US that was sending its high-ranking officials to Beijing in an effort to bring Xi to the discussion table. The White House sent officials like Blinken, Janet Yellen, and even veteran diplomat Henry Kissinger to convince Beijing to open up again. 

Had China continued its closed-window, non-responsive policy towards the US, this lack of communication could have been perceived in the US as a betrayal of the mutual commitment to peace by China.

Though this betrayal would have benefitted Beijing temporarily by avoiding diplomatic confrontation with the US, in the long run, it would have made the US more sceptical about Chinese intentions and hence more committed to preserving its own national interests. This will, in turn, lead us to the next scenario.


Once mistrust is established between the two parties due to a lack of communication, the prospects of cooperation seem superficial and potentially dangerous due to the possibility of betrayal from the opposite side, and thus paranoia takes over. In such a scenario, any nation prioritises the protection of its national interests above anything else. 

Be it in game theory or in geopolitics, the first one to betray is believed to have more advantage. In such a scenario, both nations will race to defeat each other as soon as possible. But just as in the prisoner's dilemma, mutual betrayal leads to mutual losses. The confrontation between the US and the PRC is bound to cost both sides dearly. 

Military costs: The US is at present militarily stretched out from Ukraine and Israel to the Indo-Pacific, particularly in the South China Sea. Growing conflicts and military expenditures globally are pushing the Pentagon to spend more on military aid and military deployment. In such circumstances, any mishap with China is sure to cause a huge strain on the US military and resources. 

As to China, the recent conflicts in Ukraine and Israel have shown that the military confrontation won’t be easy, will likely be prolonged, not discounting huge economic costs. This fact is more concerning for the PRC when applied to the South China Sea, which would be even more difficult than land conflicts. 

Economic costs: Despite US efforts to reduce its economic dependence on China as a major supplier and producer of US products, the US industry and big tech lobby still seem reluctant to decouple China or want more time to relocate and develop new supply chains. 

China, on the other hand, is facing an economic crisis at home due to multiple factors, from property market crises, COVID-19, and labour problems to debt overload. Adding to that, there is already a decrease in demand for Chinese exports. A full-fledged economic conflict with the US will therefore come with a heavy price.

Neither the US nor China have anything substantial to gain from betraying, and they have a lot more to lose. Thus, mutual betrayal is not a convenient option, and therefore they are left with



The Biden-Xi meeting in San Francisco took more than six months to materialise. Both sides agreed to compromise and cooperate after a thorough evaluation of the current geopolitical landscape. The US has assured China that it won’t seek to isolate Beijing, saying the world is big enough for the two nations to succeed.

While China has promised to crack down on deadly fentanyl flows to the US, both nations have agreed to reestablish military communications and have a government-to-government dialogue on emerging technologies such as AI.

This patch-up is not particularly beneficial for either nation; it is modest progress in bilateral relations that are spiralling downward. Yet this is much preferred by both Beijing and Washington over the heavy price they would have to pay for betraying each other. This is a positive-sum game scenario, as stated above. Thus, both sides have shown a rational approach in their decision-making for now.


Only time will tell us how long this cooperation lasts. But game theory can give us valuable insights into how the dynamic nature of geopolitics works between the states. The beauty of this approach is that it shows us that regardless of players and their nature, we can predict and analyse possible outcomes of a situation if we can take rationality and pragmatic decision-making as constant variables throughout all parties involved. Fortunately or unfortunately, human history does not give a guarantee for that.




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The fact that the US had to reassure China of not isolating it, and that Mr. Xi sounded appealing in trying to reassure US Companies says a lot.


Magnificent analysis of relations through game theory

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