Before revision:  Accordingly, we show that for every Nash equilibrium that is not a strong maximin equilibrium there exists a strong maximin equilibrium that Pareto dominates it. In addition, no strong maximin equilibrium is ever Pareto dominated by a Nash equilibrium. Finally, we discuss maximin equilibrium predictions in several games including the traveler's dilemma .
After revision:  Accordingly, we show that for every Nash equilibrium satisfies the optimin criterion in an auxiliary game .