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Yvain comments on Nash Equilibria and Schelling Points - Less Wrong
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"Optimal for everybody" is a very un-game-theoretic outlook. Game theorists think more in terms of "optimal for me, and screw the other guy". If everyone involved is totally selfish, and they expect other players to be pretty good at figuring out their strategy, and they don't have some freaky way of correlating their decisions with those of other agents like TDT, then they'll aim for a Nash equilibrium (though if there are multiple Nash equilibria, they might not hit the same one).
This fails either when agents aren't totally selfish (if, like you, they're looking for what's optimal for everyone, which is a very different problem), or if they're using an advanced decision theory to correlate their decisions, which is harder for normal people than it is for people playing against clones of themselves or superintelligences that can output their programs. I'll discuss this more later.
Agreed.
It's not very different - you just need to alter the agents' utility functions slightly, to value the other player gaining utility as well.
E.g. take the standard Prisoner's Dilemma: 5 for me, 0 for you if I can betray you, 3 each if we cooperate, 1 each if we defect. The equilibrium is defect / defect. Now let's make our agents' utility function look altruistic - each agent gets a reward, and then gets to add the opponent's reward as well (no loops, just add at the end.) Now our payoff is 5+0 for me, 0+5 for you if I betray you, 3+3 each if we cooperate, and 1+1 each if we defect.
A purely self-interested agent with that utility function has the equilibrium at cooperate / cooperate.
More generally, the math in games involved selfish players goes through if you represent their altruism in their own utility function, so they can act still simply pick the highest number 'selfishly' .