Well, they do, but here is the thing they are afraid of:
Before WW2 the US economy was doing poorly. The war brought a lot of war manufacturing business and huge boom in the US occurred thanks to the war production.
Economist at the time were afraid that the end of war will kill the boom because there will be no more war production needed. Well, once the war was over big US companies just switched their production capacity to civilian markets: cars manufacturing, appliances, houses construction... there was no contraction after the war. Opposite: 50s were the time of enormous economic boom.
Now, you are mistaken with setting "Prisoner dilemma" as the problem foreigners have. They may also look at their situation from the same perspective as Americans did during WW2. That is: If we stop producing for the export to the US (war effort) - there will be crisis. Who will buy our stuff but the American consumer. Well, no fear. Just switch production to your domestic markets as US did by switching industrial production to its domestic market after WW2. Nothing bad will happen with China the day "war" will be over and China will stop exporting production to the US. They will just realize that they have huge 1.3 billion consumer market at home and no need to export to the US. They will just switch production.
Therefore, Prisoner's dilemma has nothing to do with the fear of losing market based on false predictions. Nothing happened to the US market once the war was over. Nothing will happen to China once its main customer goes bankrupt.