Finding suitable solutions of strategic games is an important task in game theory. The most studied solution concept is the Nash equilibrium. However, Nash equilibria may not be Pareto efficient (e.g., in prisoner's dilemma or tragedy of the commons situations).
To reestablish Pareto efficiency, Aumann (1959, 1960) introduced strong Nash equilibria, a strengthening of Nash equilibria that requires an equilibrium strategy profile to be robust against coalitional deviations. By requiring Pareto efficiency for each coalition, Dubey (1986) introduced an even stronger refinement of the set of Nash equilibria: strict strong Nash equilibria.
Aumann, R. J. (1959). Acceptable points in general cooperative n-person games. In A. W. Tucker and R. D. Luce (Eds.), Contributions to the Theory of Games (AM-40), Volume IV, pp. 287–324. Princeton University Press.
Aumann, R. J. (1960). Acceptable points in games of perfect information. Pacific Journal of Mathematics 10(2), 381–417.
Dubey, P. (1986). Inefficiency of Nash equilibria. Mathematics of Operations Research 11 (1), 1–8.
