Before revision:  In this paper, I introduce a novel solution concept, dubbed the optimin criterion, which (to the best of my knowledge) is the first parameter-free concept that can selectively explain the direction of well-established non-Nash deviations towards cooperation in games, including the repeated prisoner's dilemma, the traveler's dilemma, the centipede game, and the repeated public goods game. Moreover, the optimin criterion generalizes and unifies results in various fields: It not only coincides with (i) Wald's statistical decision-making criterion when Nature is antagonistic, (ii) the core in cooperative games when the core is nonempty, though it exists even if the core is empty, but  also generalizes (iii) Nash equilibrium in n-person constant-sum games, (iv) stable matchings in matching models, and (v) competitive equilibrium in the Arrow-Debreu economy.
After revision:  In this paper, I introduce a novel solution concept, dubbed the optimin criterion, which is based on (Pareto) optimizing the worst-case payoffs of tacit agreements. The optimin criterion generalizes and unifies results in various fields: It not only coincides with (i) Wald's statistical decision-making criterion when Nature is antagonistic, (ii) the core in cooperative games when the core is nonempty, though it exists even if the core is empty, but also generalizes (iii) Nash equilibrium in n-person constant-sum games, (iv) stable matchings in matching models, and (v) competitive equilibrium in the Arrow-Debreu economy.