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There is something curious to me in the Prisoner's dilemma. The (mixed) Nash equilibrium is $\{(0,1);(0,1)\}$. In that notation, I mean it is the mixed strategic profile $(s_1,s_2)$ where $s_1$ and $s_2$ assign the action Silent to $0$. But if the prisoners could make a joint decision, the profile $\{(1,0);(1,0)\}$ would be the most suitable. Then I'm wondering in which sense the Nash equilibrium is more interesting that the last profile. In general lines, it is easy to find important applications of Nash equilibrium. But I would like to compare its importance to the one of the profile that represents the best joint decision profile, that is, the profile that provides recompenses with the minimum variance possible and the maximum sum of gains. If someone could help, I'd be grateful. Thanks in advance!

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    $\begingroup$ A Nash equilibrium is important if we want to model our players as selfish: who cares about recompenses with the minimum variance possible and the maximum sum of gains when you want the biggest payoff for yourself? If you can improve your outcome unilaterally, why wouldn't you? $\endgroup$ – Omnomnomnom Jun 16 '17 at 13:46
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In the spirit of the above comment, Nash equilibrium is, at first glance (and certainly was in the early days of game theory) the only normatively reasonable notion of what the solution to a non-cooperative problem should look like.

Previously people had discussed the far simpler 'decision theory' whereby some agent simply tries to do as best as they might in the face of exogenous uncertainty: man versus nature. Game theory is considerably more challenging for the obvious reason that rather than nature one is up against an equally intelligent optimizing figure whose incentives may be arbitrarily poorly aligned with ones own. To that effect, the idea of a set of choices of action that is robust against unilateral deviation is the natural specification one is led toward when searching for an answer to the question "how will this encounter turn out."

As the commenter stated: in such circumstances, why should I sacrifice my own well-being for the good of the whole? And given I feel this way, why should I trust you to do the same for me when my payoff hangs in the balance? It does not take much time in the world to realize this is probably a better model of human reasoning than playing nicely together.

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