If I understood your description. The reasoning you have given is already assumed in Nash equilibrium.
That is to say, regarding the equilibrium concept of Nash, even though everybody knows everybody else's strategy nobody wants to deviate from her strategy in a Nash equilibrium. So there is no benefit for someone to change her strategy. Note that everybody knows that everybody knows that everybody is rational, i.e. common knowledge is common knowledge as well.
What is not assumed in Nash equilibrium is the following. It is not allowed for players to form coalitions. That is, two or more players can not act together to improve their payoff. But as you say "changing one's strategy" I do not think forming coalitions is what you mean. If so, then you can check "cooperative game theory".