Paretooptimalitet

Paretooptimalitet, or Pareto efficiency, is a concept in economics and game theory describing an allocation of resources among agents such that no reallocation could improve at least one agent’s outcome without making someone else worse off. The term is named after vilfredo Pareto, who introduced ideas about efficiency in resource use and welfare.

Formally, let X be the feasible set of allocations and let u_i(x) denote the utility of agent i under allocation x. An allocation x* in X is Pareto optimal if there is no x in X such that u_i(x) ≥ u_i(x*) for all i, with strict inequality for at least one i. If such an x exists, x* is not Pareto efficient and a Pareto improvement is possible. The collection of Pareto efficient allocations forms the Pareto frontier.

Key properties include that multiple Pareto efficient allocations can exist, reflecting trade-offs between agents. Pareto optimality does not prescribe fairness or distributional goals; it only requires that no further Pareto improvements are possible. It is thus a local criterion rather than a complete welfare ordering, and different welfare criteria (utilitarian, Rawlsian, etc.) may rank Pareto efficient allocations differently.

Applications and extensions of the concept are widespread in policy analysis, market design, and mechanism design. Related notions include weak and strong Pareto efficiency, the core, and the First Welfare Theorem, which states that under certain conditions a competitive equilibrium is Pareto efficient.