Stationary solution of thought

Suppose person X acts in a certain way. Now, person Y gets to know about X’s action and interprets it in some way. Now if X understands how Y will interpret his action, then this will influence his actions. But, if Y also understands that X would know how the action will be interpreted by him, then he would interpret X’s action in a different way, under the conditioning of awareness of X. And, if this process goes on and on, we get a stationary or an equilibrium solution of thought, which decides how X will act eventually. But, if the state space is discrete, then the solution may be oscillatory. For example, suppose my brother and I have a comic book, which we both want to take to school for reading.  The comic can be either in a shelf or in a bag. But, the school bus leaves in a minute, and so my brother can search for the comic at only one place. Now, if I know where the comic is and he asks me about it. Then, no matter what my answer is, the stationary solution of his interpretation will be oscillatory in nature.