Pareto Efficiency

When can everyone be made better off — and why equilibria can waste.

The idea

Pareto efficiency is the standard test for whether an outcome wastes welfare: an outcome fails it exactly when some other available outcome helps somebody and hurts nobody.

Compare outcomes by the payoffs they give. Outcome $y$ Pareto dominates outcome $x$ when every player is at least as well off under $y$ as under $x$, and at least one player is strictly better off. Both clauses matter. "At least as well off for everyone" rules out changes that merely transfer payoff from one player to another, however large the winner's gain. "Strictly better for someone" rules out counting an outcome as an improvement on itself. Plotted by their payoff pairs, $y$ Pareto dominates $x$ exactly when $y$ lies up and to the right of $x$, strictly so in at least one direction.

An outcome is Pareto efficient when no available outcome Pareto dominates it.

Efficiency is not fairness: an outcome giving one player everything and another nothing is efficient as soon as the favored player cannot be improved, because helping the other must take something from them. Efficiency is not equilibrium either: an outcome from which no player wants to deviate unilaterally can still be Pareto dominated, and the two verdicts routinely disagree.

Ways to work on it

• Walkthrough. Pareto efficiency and domination, illustrated by the Prisoner's Dilemma.
• Practice. Decide whether one outcome Pareto dominates another.
• Hardest. Count efficient outcomes of a game and contrast with its equilibrium.

Not sure where to start? Take the ten-question placement test.