Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after Vilfredo Pareto (1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related:
Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose. A situation is called Pareto-dominated if there exists a possible Pareto improvement. A situation is called Pareto-optimal or Pareto-efficient if no change could lead to improved satisfaction for some agent without some other agent losing or, equivalently, if there is no scope for further Pareto improvement (in other words, the situation is not Pareto-dominated).
The Pareto front (also called Pareto frontier or Pareto set) is the set of all Pareto-efficient situations.
Pareto originally used the word "optimal" for the concept, but as it describes a situation where a limited number of people will be made better off under finite resources, and it does not take equality or social well-being into account, it is in effect a definition of and better captured by "efficiency".
In addition to the context of efficiency in allocation, the concept of Pareto efficiency also arises in the context of efficiency in production vs. x-inefficiency: a set of outputs of goods is Pareto-efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.
Pareto efficiency is measured along the production possibility frontier (PPF), which is a graphical representation of all the possible options of output for two products that can be produced using all factors of production.
Besides economics, the notion of Pareto efficiency has been applied to the selection of alternatives in engineering and biology. Each option is first assessed, under multiple criteria, and then a subset of options is ostensibly identified with the property that no other option can categorically outperform the specified option. It is a statement of impossibility of improving one variable without harming other variables in the subject of multi-objective optimization (also termed Pareto optimization).
Overview
Formally, a state is Pareto-optimal if there is no alternative state where improvements can be made to at least one participant's well-being without reducing any other participant's well-being. If there is a state change that satisfies this condition, the new state is called a "Pareto improvement". When no Pareto improvements are possible, the state is a "Pareto optimum".
In other words, Pareto efficiency is when it is impossible to make one party better off without making another party worse off. This state indicates that resources can no longer be allocated in a way that makes one party better off without harming other parties. In a state of Pareto Efficiency, resources are allocated in the most efficient way possible.
Pareto efficiency is mathematically represented when there is no other strategy profile s such that ui (s') ≥ ui (s) for every player i and uj (s') > uj (s) for some player j. In this equation s represents the strategy profile, u represents the utility or benefit, and j represents the player.
Efficiency is an important criterion for judging behavior in a game. In a notable and often analyzed game known as Prisoner's Dilemma, depicted below as a normal-form game, this concept of efficiency can be observed, in that the strategy profile (Cooperate, Cooperate) is more efficient than (Defect, Defect).
Using the definition listed above, u(Ci) ≥ u(Di) for i ∈ { 1, 2}, thus yielding this strategy as a Pareto efficient strategy. In other words, both players receive an increase in payoff by selecting Cooperate over Defect.
In zero-sum games, every outcome is Pareto-efficient.