A great example of uselessness of game theory in real life situations though.
For one, it equates the choices - long-term and short-term, conservative and progressive, moral and ethical, economic and social...
E.g. There wasn't a WW3 with China OR Soviet Union spurred on by a myth of genetic superiority and bloodlines built-into the leftist ideology. Right-wing ideology will always boil down to such a myth.
For two, it assumes a whole bunch of other things, not just the choices being essentially identical.
From a 100% voter turn-out of perfectly informed and rational spherical voters to complete absence of propaganda and the influence of money on campaigning.
FFS Haven't we learned that people would rather poison themselves with horse deworming paste than listen to reason?
But most importantly - it presumes that the most favorable outcome is some centrist position between the extremes, which will magically be free of influence from either extreme, while ignoring the reality of the "wild card" of fascism.
I.e. That it is a bullshit ideology completely fine with lying and cheating in order to seize the power.
Thus while in theory such a system would result in "the moderate that everyone liked" - in reality everyone HATES such a moderate (Hint: Both Al Gore and Hillary Clinton would have been that choice - both were hated for made up reasons such as "being a robot" and "not baking cookies".) - and you end up with a far right candidate who is willing to lie and cheat to win.