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Encyclopedia > Pareto efficiency

Pareto efficiency, or Pareto optimality, is an important notion in neoclassical economics with broad applications in game theory, engineering and the social sciences. The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution. Neoclassical economics refers to a general approach (a metatheory) to economics based on supply and demand which depends on individuals (or any economic agent) operating rationally, each seeking to maximize their individual utility or profit by making choices based on available information. ... Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns. ... Engineering is the design, analysis, and/or construction of works for practical purposes. ... The social sciences are a group of academic disciplines that study human aspects of the world. ... Vilfredo Federico Damaso Pareto [vilfre:do pare:to] (July 15, 1848, Paris – August 19, 1923, Geneva) was a French-Italian sociologist, economist and philosopher. ... Economic efficiency is a general term for the value assigned to a situation by some measure designed to capture the amount of waste or friction or other undesirable economic features present. ... This graphic shows the distribution of gross annual household income. ...


Given a set of alternative allocations and a set of individuals, a movement from one allocation to another that can make at least one individual better off, without making any other individual worse off, is called a Pareto improvement or Pareto optimization. An allocation of resources is Pareto efficient or Pareto optimal when no further Pareto improvements can be made. In economics, factors of production are resources used in the production of goods and services. ...


A strongly Pareto optimal (SPO) allocation (X) is one for which there cannot be any other feasible allocation (say X') such that the allocation (X') is strictly preferred by at least one person, and weakly preferred (not opposed) by everyone else. A (weakly) Pareto optimal (WPO) allocation is one where there is no feasible reallocation that would be strictly preferred by all agents.

Contents

Pareto frontier

Example of Pareto frontier, given that lower values are preferred to higher values. Point C is not on the Pareto Frontier because it is dominated by both point A and point B. Points A and B are non-inferior.
Example of Pareto frontier, given that lower values are preferred to higher values. Point C is not on the Pareto Frontier because it is dominated by both point A and point B. Points A and B are non-inferior.

For a given system, the Pareto frontier or Pareto set is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused tradeoffs within this constrained set of parameters, rather than needing to consider the full ranges of parameters. Image File history File links Front_pareto. ... Image File history File links Front_pareto. ...


The Pareto frontier, P(Y), may be more formally described as follows. Consider a system with function f: mathbb{R}^n rightarrow mathbb{R}^m, where X is a compact set of feasible decisions in the metric space mathbb{R}^n, and Y is the feasible set of criterion vectors in mathbb{R}^m, such that . In mathematics, a subset of Euclidean space Rn is called compact if it is closed and bounded. ... In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ...


We assume that the preferred directions of criteria values are known. A point is preferred to (strictly dominating) another point y^{prime} in mathbb{R}^m;, written as y^{primeprime} succ y^{prime}. The Pareto frontier is thus written as:


P(Y) = { y^{prime} in Y: ; {y^{primeprime} in Y:; y^{primeprime} succ y^{prime}, y^{primeprime} neq y^{prime} ; } = empty } .


Pareto efficiency in economics

If an economic system is Pareto efficient, then it is the case that no individual can be made better off without another being made worse off. It is commonly accepted that outcomes that are not Pareto efficient are to be avoided, and therefore Pareto efficiency is an important criterion for evaluating economic systems and public policies. This article does not cite any references or sources. ...


If economic allocation in any system (in the real world or in a model) is not Pareto efficient, there is theoretical potential for a Pareto improvement - an increase in Pareto efficiency: through reallocation, improvements to at least one participant's well-being can be made without reducing any other participant's well-being.


In the real world ensuring that nobody is disadvantaged by a change aimed at improving economic efficiency may require compensation of one or more parties. For instance, if a change in economic policy dictates that a legally protected monopoly ceases to exist and that market subsequently becomes competitive and more efficient, the monopolist will be made worse off. However, the loss to the monopolist will be more than offset by the gain in efficiency. This means the monopolist can be compensated for its loss while still leaving an efficiency gain to be realised by others in the economy. Thus, the requirement of nobody being made worse off for a gain to others is met.


In real-world practice, the compensation of the monopolist (or other loser) is hardly ever made. It is left hypothetical. The change is thus not Pareto efficient. The theory of hypothetical compensation is part of the Kaldor-Hicks concept of efficiency. Kaldor-Hicks efficiency is a type of economic efficiency that occurs only if the economic value of social resources is maximized. ...


Under certain idealised conditions, it can be shown that a system of free markets will lead to a Pareto efficient outcome. This was first demonstrated mathematically by economists Kenneth Arrow and Gerard Debreu. This is called the first welfare theorem. However, the result likely does not reflect the workings of real economies because of the restrictive assumptions necessary for the proof (markets exist for all possible goods, markets are perfectly competitive, transaction costs are negligible, and there must be no externalities). A free market is an idealized market, where all economic decisions and actions by individuals regarding transfer of money, goods, and services are voluntary, and are therefore devoid of coercion and theft (some definitions of coercion are inclusive of theft). Colloquially and loosely, a free market economy is an economy... Kenneth Joseph Arrow (born August 23, 1921) is an American economist, joint winner of the Nobel Prize in Economics with John Hicks in 1972, and the youngest person ever to receive this award, at 51. ... Gerard Debreu was a naturalized US citizen from France Gerard Debreu (July 4, 1921 – December 31, 2004) was a French economist and mathematician (In July 1975, he became a naturalized citizen of the United States). ... In welfare economics, the First Welfare Theorem is that a system of free markets will lead to a Pareto efficient equilibrium. ... In economics, an externality is a cost or benefit resulting from an economic transaction that is borne or received by parties not directly involved in the transaction. ...


A key drawback of Pareto optimality is its localisation and partial ordering. In an economic system with millions of variables there can be very many local optimum points. The Pareto improvement criterion does not define any global optimum. Given a reasonable criterion which compares all points, many Pareto-optimal solutions may be far inferior to the global best solution. In mathematics, a partially ordered set (or poset for short) is a set equipped with a special binary relation which formalizes the intuitive concept of an ordering. ... Polynomial of degree 4, on the right one finds a local optimum, on the left is the global optimum. ...


Relationship to marginal rate of substitution

An important fact about the Pareto frontier in economics is that at a Pareto efficient allocation, the marginal rate of substitution is the same for all consumers. A formal statement can be derived by considering a system with m consumers and n goods, and a utility function of each consumer as zi = fi(xi) where x^i=(x_1^i, x_2^i, ldots, x_n^i) is the vector of goods, both for all i. The supply constraint is written sum_{i=1}^m x_j^i = b_j^0 for j=1,ldots,n. To optimize this problem, the Lagrangian is used: A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a function of the dynamical variables and concisely describes the equations of motion of the system. ...


L(x, lambda, Gamma)=f^1(x^1)+sum_{i=2}^m lambda_i(z_i^0 - f^i(x^i))+sum_{j=1}^n Gamma_j(b_j^0-sum_{i=1}^m x_j^i) where λ and Γ are multipliers.


Taking the partial derivatve of the Lagrangian with respect to one good, i, and then taking the partial derivative of the Lagrangian with respect to another good, j, gives the following system of equations:


frac{partial L}{partial x_j^i} = f_{x^1}^1-Gamma_j^0=0 for j=1,...,n. frac{partial L}{partial x_j^i} = -lambda_i^0 f_{x^1}^1-Gamma_j^0=0 for i = 2,...,m and j=1,...,m, where fx is the marginal utility on f' of x (the partial derivative of f with respect to x).


Rearranging these to eliminate the multipliers gives the wanted result:


frac{f_{x_j^i}^i}{f_{x_s^i}^i}=frac{f_{x_j^k}^k}{f_{x_s^k}^k} for i,k=1,...,m and j,s=1,...,n.


Criticisms

Pareto efficiency does not require an equitable distribution of wealth. An economy in which the wealthy hold the vast majority of resources can be Pareto efficient. This should, of course, not be understood as criticism of Pareto efficiency itself, but rather of the idea that Pareto efficiency is desirable or even only Pareto efficiency is desirable. This point has been strongly made by Michele Piccione and Ariel Rubinstein in their paper, Equilibrium in the Jungle, which shows that outcomes in a world where strong agents may steal goods from weaker agents are efficient. Ariel Rubinstein (born April 13, 1951) is an economist who works in game theory. ...


Amartya Sen has elaborated the mathematical reasons for this criticism, pointing out that under relatively plausible starting conditions, systems of social choice will converge on Pareto efficient, but inequitable, distributions. A simple example is dividing a pie into pieces to distribute among three people. The most equitable distribution is each person getting one third. However the solution of two people getting half a pie and the third person getting none is also Pareto optimal despite not being equitable, because the only way for the person with no piece to get a piece is for one or both of the other two to get less, which is not a Pareto improvement. A Pareto inefficient distribution of the pie might be each person getting one-quarter of the pie with the remainder discarded. Of course, this example completely ignores the origin of the pie, so it breaks down to the criticism that Pareto efficiency does not really help in determining the optimal allocation of windfalls that nobody involved actually produced, such as land, inherited wealth, broadcast spectrum, the environment, or a pie miraculously falling from the sky. This article does not cite any references or sources. ... Social choice theory studies how individual preferences are aggregated to form a collective preference. ...


A more generalized form of this criticism lies in the definition of Pareto efficiency itself. By requiring that no participants be worse off, Pareto efficiency protects the status quo and therefore any inequity or other problems currently existing. Status Quo are an English rock band whose music is characterised by a strong boogie line. ...


See also

The compensation principle in welfare economics refers to a decision rule used to select between pairs of alternative feasible social states. ... In economics, a deadweight loss (also known as excess burden) is a permanent loss of well being to society that can occur when equilibrium for a good or service is not Pareto optimal, (that at least one individual could be made better off without others being made worse off). ... Economic efficiency is a general term for the value assigned to a situation by some measure designed to capture the amount of waste or friction or other undesirable economic features present. ... The liberal paradox is a logical paradox advanced by Amartya Sen, building on the work of Kenneth Arrow and his general possibility theorem, which showed that within a system of menu-independent social choice, it is impossible to have both a commitment to Minimal Liberty, which was defined as the... There exists two fundamental theorems of welfare economics. ... Kaldor-Hicks efficiency is a type of economic efficiency that occurs only if the economic value of social resources is maximized. ... Multidisciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. ... Multi-objective optimization (or programming),[1][2] also known as multi-criteria or multi-attribute optimization, is the process of simultaneously optimizing two or more conflicting objectives subject to certain constraints. ... There are very few or no other articles that link to this one. ... Kenneth Arrows monograph Social Choice and Individual Values (1951, 2nd ed. ... Welfare economics is a branch of economics that uses microeconomic techniques to simultaneously determine the allocational efficiency of a macroeconomy and the income distribution associated with it. ... Abram Bergson, born Abram Burk (April 21, 1914, New York City - April 23, 2003), was an American economist. ...

References

  • Fudenberg, D. and Tirole, J. (1983). Game Theory. MIT Press, Chapter 1, Section 2.4. 
  • Osborne, M.J. and Rubenstein, A. (1994). A Course in Game Theory. MIT Press, p. 7. ISBN 0-262-65040-1. 


Jean Tirole (born 9 August 1953) is a notable contemporary french economist, author of many works in economics, scientific director of the Industrial Economics Institute in Toulouse. ... Ariel Rubenstein (born April 13, 1951) is an economist who works in game theory. ...

 view  Topics in game theory

Definitions Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns. ...

Normal form game · Extensive form game · Cooperative game · Information set · Preference In game theory, normal form is a way of describing a game. ... It has been suggested that Game tree be merged into this article or section. ... A cooperative game is a game where groups of players (coalitions) may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players. ... In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed so far. ... Preference (or taste) is a concept, used in the social sciences, particularly economics. ...

Equilibrium concepts Price of market balance In economics, economic equilibrium is simply a state of the world where economic forces are balanced and in the abscence of external shocks the (equilibrium) values of economic variables will not change. ... In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...

Nash equilibrium · Subgame perfection · Bayesian-Nash · Perfect Bayesian · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · Risk dominance In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ... Subgame perfect equilibrium is an economics term used in game theory to describe an equilibrium such that players strategies constitute a Nash equilibrium in every subgame of the original game. ... In game theory, a Bayesian game is one in which information about characteristics of the other players (i. ... In game theory, a Bayesian game is one in which information about characteristics of the other players (i. ... The trembling hand perfection is a notion that eliminates actions of players that are unsafe because they were chosen through a slip of the hand. ... Proper equilibrium is a refinement of Nash Equilibrium due to Roger B. Myerson. ... In game theory, an Epsilon-equilibrium is a strategy profile that approximately satisfies the condition of Nash Equilibrium. ... In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. ... Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson. ... Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme. ... In game theory, an evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a strategy which if adopted by a population cannot be invaded by any competing alternative strategy. ... Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten. ...

Strategies In game theory, a players strategy, in a game or a business situation, is a complete plan of action for whatever situation might arise; this fully determines the players behaviour. ...

Dominant strategies · Mixed strategy · Tit for tat · Grim trigger · Collusion In game theory, dominance occurs when one strategy is better or worse than another regardless of the strategies of a players opponents. ... In game theory a mixed strategy is a strategy which chooses randomly between possible moves. ... Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ... Grim Trigger is a trigger strategy in game theory for a repeated game, such as an iterated prisoners dilemma. ... Look up collusion in Wiktionary, the free dictionary. ...

Classes of games

Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design · Stochastic game · Nontransitive game In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. ... Perfect information is a term used in economics and game theory to describe a state of complete knowledge about the actions of other players that is instantaneously updated as new information arises. ... In game theory, a sequential game is a game where one player chooses his action before the others chooses theirs. ... In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ... Signaling games are dynamic games with two players, the sender (S) and the receiver (R). ... Cheap Talk is a term used in Game Theory for pre-play communication which carries no cost. ... Zero-sum describes a situation in which a participants gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). ... Mechanism design is a sub-field of game theory. ... In game theory, a stochastic game is a competitive game with probabilistic transitions played by two players. ... A non-transitive game is a game for which the various strategies produce one or more loops of preferences. ...

Games Game theory studies strategic interaction between individuals in situations called games. ...

Prisoner's dilemma · Traveler's dilemma · Coordination game · Chicken · Volunteer's dilemma · Dollar auction · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game · Public goods game · Nash bargaining game · Blotto games  · War of attrition Will the two prisoners cooperate to minimize total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In game theory, the prisoners dilemma (sometimes abbreviated PD) is a type of non-zero-sum game in which two players... In game theory, the travelers dilemma (sometimes abbreviated TD) is a type of non-zero-sum game in which two players attempt to maximise their own payoff, without any concern for the other players payoff. ... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... The game of Chicken, also known as the Hawk-Dove game, is an influential model of conflict for two players in game theory. ... The Volunteers dilemma game models a situation in which each of N players faces the decision of either making a small sacrifice from which all will benefit or freeriding. ... On eBay, where an auction has a starting price of $1 ... The Battle of the Sexes is a two player game used in game theory. ... In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. ... Matching Pennies is the name for a simple example game used in game theory. ... The Ultimatum game is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. ... Minority Game is a game proposed by Yi-Cheng Zhang and Damien Challet from the University of Fribourg. ... Rock, Paper, Scissors chart Listen to this article ( info) in media player in browser This audio file was created from an article revision dated 2006-07-13, and may not reflect subsequent edits to the article. ... From Howard Pyles Book of Pirates The pirate game is a simple mathematical game. ... The dictator game is a very simple game in experimental economics, similar to the ultimatum game. ... The Public goods game is a standard of experimental economics; in the basic game subjects secretly choose how many of their private tokens to put into the public pot. ... The Nash Bargaining Game is a simple two player game used to model bargaining interactions. ... Blotto games (or Colonel Blotto games) constitute a class of two-person zero-sum games in which the players are tasked to simultaneously distribute limited resources over several objects, with the gain (or payoff) being equal to the sum of the gains on the individual objects. ... In game theory the War of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while accumulating costs at a constant rate c. ...

Theorems

Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's Theorem Minimax (sometimes minmax) is a method in decision theory for minimizing the maximum possible loss. ... In game theory, the purification theorem was contributed by Nobel laurate John Harsanyi in 1973[1]. The theorem aims to justify a puzzling aspect of mixed strategy Nash equilibria: that each player is wholly indifferent amongst each of the actions he puts non-zero weight on, yet he mixes them... In game theory, folk theorems are a class of theorems which imply that in repeated games, any outcome is a feasible solution concept, if under that outcome the players minimax conditions are satisfied. ... The revelation principle of economics can be stated as, To any equilibrium of a game of incomplete information, there corresponds an associated revelation mechanism that has an equilibrium where the players truthfully report their types. ... In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox demonstrates the impossibility of designing a set of rules for social decision making that would meet all of a certain set of criteria. ...

Related topics

Mathematics · Mathematical programming · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists · Social trap · Tragedy of the commons Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... In mathematics, the term optimization refers to the study of problems that have the form Given: a function f : A R from some set A to the real numbers Sought: an element x0 in A such that f(x0) ≤ f(x) for all x in A (minimization) or such... Face-to-face trading interactions on the New York Stock Exchange trading floor. ... Nobel Prize in Economics winner Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ... Evolutionary game theory (EGT) is the application of game theory in evolutionary biology. ... Population genetics is the study of the distribution of and change in allele frequencies under the influence of the four evolutionary forces: natural selection, genetic drift, mutation, and migration. ... Behavioral ecology is the study of the ecological and evolutionary basis for animal behavior, and the roles of behavior in enabling an animal to adapt to its environment (both intrinsic and extrinsic). ... Adaptive Dynamics is a set of techniques for studying long-term phenotypical evolution developed during the 1990s. ... This is a list of notable economists, mathematicians, political scientists, and computer scientists whose work has added substantially to the field of game theory. ... Social trap is a term used by psychologists to describe a situation in which a group of people act to obtain short-term individual gains, which in the long run leads to a loss for the group as a whole. ... It has been suggested that Tyranny of the Commons be merged into this article or section. ...


  Results from FactBites:
 
The Pareto Principle - The 80/20 rule (512 words)
In 1906, Italian economist and sociologist, Vilfredo Pareto (sometimes misspelled Wilfredo, Alfredo, or Vilfred) created a mathematical formula to describe the uneven income distribution in Switzerland at that time, observing that eighty percent of the wealth was held by a mere twenty percent of the families.
Because Pareto's initial discovery involved a distribution of 80% of wealth to 20% of families and it's inverse, the Pareto Principle is often called "The 80/20 rule".
Pareto's Principle, or the 80/20 Rule, should serve as a continual reminder to focus eighty percent of your effort on the twenty percent of your tasks that matter the most.
Reference.com/Encyclopedia/Pareto efficiency (1159 words)
Pareto efficiency, or Pareto optimality, is an important notion in neoclassical economics with broad applications in game theory, engineering and the social sciences.
It is commonly accepted that outcomes that are not Pareto efficient are to be avoided, and therefore Pareto efficiency is an important criterion for evaluating economic systems and public policies.
An important fact about the Pareto frontier in economics is that at a Pareto efficient allocation, the marginal rate of substitution is the same for all consumers.
  More results at FactBites »

 
 

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