  Since the 1990s, artificial intelligence (AI) systems have achieved
'superhuman performance' in major zero-sum games, where winning has an
unambiguous definition. However, most economic and social interactions are
non-zero-sum, where measuring 'performance' is a non-trivial task. In this
paper, I introduce a novel benchmark, super-Nash performance, and a solution
concept, optimin, whereby every player maximizes their minimal payoff under
unilateral profitable deviations of the others. Optimin achieves super-Nash
performance in that, for every Nash equilibrium, there exists an optimin where
each player not only receives but also guarantees super-Nash payoffs, even if
other players deviate unilaterally and profitably from the optimin. Further,
optimin generalizes and unifies several key results across domains: it
coincides with (i) the maximin strategies in zero-sum games, and (ii) the core
in cooperative games when the core is nonempty, though it exists even if the
core is empty; additionally, optimin generalizes (iii) Nash equilibrium in
$n$-person constant-sum games. Finally, optimin is consistent with the
direction of non-Nash deviations in games in which cooperation has been
extensively studied, including the finitely repeated prisoner's dilemma, the
centipede game, the traveler's dilemma, and the finitely repeated public goods
game.
