Game theory damages self interest

Individuals thinking in their own interest can lead to good outcomes for all, but when game theory dynamics comes into play sometimes your own individual best outcomes can be worse overall for people.

It's in your own interest to not pay tax and have other people pay tax for policing/army. Even if only a low percentage paid tax damaging the government's ability to police effectively, it's still in your best interest to not pay tax. If everyone took the best possible position to not pay tax outcomes over all could be worse than if everyone took the worse position for themselves.

Game theory tactics are also evident on national scales, it's generally good for countries to think about themselves but when game theory dynamics come into play it's best to have agreements between countries or a higher authority enforcing the best outcome as it can be difficult to get multiple parties to agree.
This can be seen with CO2 emissions and in nuclear warfare. If a country has a nuclear weapon aimed at you it's in your best interest to have a nuclear weapon aimed at them, but if agreement can be met it's best for you both to agree to get rid of your nuclear weapons.