You're right about "everyone should participate in the system, only taking into account their own success and profit, and nothing more than that" being (at least part of) the root problem. However, this is not a description of a Nash equilibrium. It uses the word “should”. It's a philosophy. It is, in fact, the philosophy of capitalism. It creates incentives for short-term thinking, profit-seeking at the detriment to the public good, and competition in areas where collaboration is more appropriate. It doesn't have to be that way, no matter how much the rich and powerful less us that it should.
A Nash equilibrium is a state of affairs in which no single person can improve their position without the collaboration of others. A frequently cited example is a bank run: if the bank goes bust, you better get your savings out quickly, but if everyone does it, the bank goes bust. The solution is for everyone to cooperate and agree to refrain from a run on the bank. Such collaboration is not easy to organize and not easy to convince a majority to participate in; but the ego-centric philosophy of capitalism makes it infinitely harder.
A Nash equilibrium is a state of affairs in which no single person can improve their position without the collaboration of others. A frequently cited example is a bank run: if the bank goes bust, you better get your savings out quickly, but if everyone does it, the bank goes bust. The solution is for everyone to cooperate and agree to refrain from a run on the bank. Such collaboration is not easy to organize and not easy to convince a majority to participate in; but the ego-centric philosophy of capitalism makes it infinitely harder.