A Nash equilibrium need not be Pareto optimal,and a Pareto-optimal outcome need not be a Nash equilibrium.

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A Nash equilibrium means that no player can improve their outcome by unilaterally changing their strategy, but this does not necessarily mean that the outcome is optimal for everyone involved. On the other hand, a Pareto-optimal outcome means that no one can be made better off without making someone else worse off, but this does not necessarily mean that the players' strategies are in equilibrium and no one has an incentive to deviate.

A Nash Equilibrium Need Not Be Pareto Optimal,and a Pareto-Optimal