Game Theory and US – China Trade War
In a Hawk-Dove Game, two animals fight for a piece of food. Each animal can choose the Hawk strategy to fight aggressively or the Dove strategy to fight passively. If they both behave passively, they divide the food evenly. If one of them fight aggressively and the other fights passively, the aggressive one will get more food and the passive on will get less, but not none at all. If they both fight aggressively, neither of them get food. The equilibrium strategy pair is one fights aggressively and one fights passively (no matter which one, so actually two equilibria). 
In the US-China Trade War, everything started with President Trump charging duties on Chinese imports and China responded without any concessions. Looking at the situation theoretically, they both have two choices: one is to continue escalating the fight and one is back down. According to the current loss on both sides, there is definitely more pain than gain during the whole process for both sides, including job loss, decreasing GDP, and slower growth of technologies, etc. Its payoff matrix seems to be simple. If they both fight, both lose. If they both back down, win-win. If one of them fights and the other backs down, the aggressive one achieves more, probably more than in the both-back-down win-win situation. This is exactly like the Hawk-Dove Game.
No side was willing to back down at the beginning. The trade war extended to politics, education and everything in real life. During COVID, their travel bans stopped people from “opponent” country to enter. When President Trump started the “war”, he probably believed that China could be Dove, like Korea or Japan decades ago. When President Xi fought back, he probably did not want to be Dove anymore and fought back even though he knew this would cause damage to both sides. In theory, if America chooses to be Hawk, the best response for China is to be Dove. Vice versa. In terms of current economic gains, this is correct. But we have to consider other factors. For example, being a Dove not only means less benefits than Hawk, but also means less benefits than before, which is definitely unacceptable for any one who has the ability to fight back. Also, being a Dove not only means compromising for now, but also means concessions in long run. Hawk is always Hawk and Dove will never become a Hawk. Countries are not like animals, they are ambitious. The Dove does not want to be Dove forever but the Hawk does want to be Hawk forever. China has to maintain its dignity and the US has to maintain its leading position. So they will never be satisfied with the two game equilibria.
Recently, their relationship started to melt. High level talks took place. Let’s look forward to their further dialogue. Hope they can arrive at a position where both parties are satisfied. Probably not an absolutely equal win-win between two Doves, but hopefully an equilibrium that can be maintained, even if a temporary one.
Source: https://www.bloomberg.com/news/articles/2018-06-21/game-theory-explains-why-the-u-s-china-trade-spat-is-worsening