Pareto efficiency, or Pareto optimality, is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off. The term is named after Vilfredo Pareto (1848–1923), an Italian economist who used the concept in his studies of economic efficiency and income distribution. The concept has applications in academic fields such as economics and engineering. For example, suppose there are two consumers A & B and only one resource X. Suppose X is equal to 20. Pareto efficiency is a minimal notion of efficiency and does not necessarily result in a socially desirable distribution of resources: it makes no statement about equality, or the overall well-being of a society. The notion of Pareto efficiency can also be applied to the selection of alternatives in engineering and similar fields. Pareto efficiency in short It is commonly accepted[by whom?] Weak Pareto efficiency for each i and
Nash equilibriumIn game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy. If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitutes a Nash equilibrium. The reality of the Nash equilibrium of a game can be tested using experimental economics method. Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision while Will's decision remains unchanged, and Will is making the best decision he can, taking into account Amy's decision while Amy's decision remains unchanged. Applications History The Nash equilibrium was named after John Forbes Nash, Jr. Let .
Pareto distributionThe Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power law probability distribution that is used in description of social, scientific, geophysical, actuarial, and many other types of observable phenomena. Definition If X is a random variable with a Pareto (Type I) distribution, then the probability that X is greater than some number x, i.e. the survival function (also called tail function), is given by where xm is the (necessarily positive) minimum possible value of X, and α is a positive parameter. Properties Cumulative distribution function From the definition, the cumulative distribution function of a Pareto random variable with parameters α and xm is When plotted on linear axes, the distribution assumes the familiar J-shaped curve which approaches each of the orthogonal axes asymptotically. Probability density function It follows (by differentiation) that the probability density function is Suppose
Pareto Optimal | Pareto Efficient | Pareto Improvement | Pareto TutorialPareto Efficient and Pareto Optimal Tutorial The main tenant of economics is that resources are scarce. Due to scarcity, that means that not everyone can have some of everything, leading to competition. Pareto Efficiency Named for an Italian economist who specialized in resource and income allocation, Pareto Efficiency goes hand in hand with the Pareto Optimal concept. Through making Pareto Improvements, overall social utility can be increased, by seeking to make allocation decisions that minimize decreased utility for other individuals in the efforts to increase one individual’s utility. What is Pareto Optimality Looking at a standard production possibilities frontier, all points that lie under the curve are inefficient allocations. Pareto Optimality is used heavily in political economics as a means to distribute resources in a more efficient manner to increase overall social utility. ShareThis
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Vilfredo ParetoVilfredo Federico Damaso Pareto (born Wilfried Fritz Pareto; Italian: [vilˈfreːdo paˈreːto]; 15 July 1848 – 19 August 1923) was an Italian engineer, sociologist, economist, political scientist, and philosopher. He made several important contributions to economics, particularly in the study of income distribution and in the analysis of individuals' choices. He was also responsible for popularising the use of the term "elite" in social analysis. He introduced the concept of Pareto efficiency and helped develop the field of microeconomics. His legacy as an economist was profound. Biography Pareto was born of an exiled noble Genoese family in 1848 in Paris, the centre of the popular revolutions of that year. From Civil engineer to liberal, and then to economist For some years after graduation, he worked as a civil engineer, first for the state-owned Italian Railway Company and later in private industry. He did not begin serious work in economics until his mid-forties.
What is Pareto Efficiency?Folk theorem (game theory)For an infinitely repeated game, any Nash equilibrium payoff must weakly dominate the minmax payoff profile of the constituent stage game. This is because a player achieving less than his minmax payoff always has incentive to deviate by simply playing his minmax strategy at every history. The folk theorem is a partial converse of this: A payoff profile is said to be feasible if it lies in the convex hull of the set of possible payoff profiles of the stage game. The folk theorem states that any feasible payoff profile that strictly dominates the minmax profile can be realized as a Nash equilibrium payoff profile, with sufficiently large discount factor. For example, in the Prisoner's Dilemma, both players cooperating is not a Nash equilibrium. In mathematics, the term folk theorem refers generally to any theorem that is believed and discussed, but has not been published. where ui is player i's utility in the constituent stage game G. 1. 2. 3. 2. 3. 4. 5. Jump up ^ Myerson, Roger B.
Henri LefebvreHenri Lefebvre (French: [ləfɛvʁ]; 16 June 1901 – 29 June 1991) was a French Marxist philosopher and sociologist, best known for pioneering the critique of everyday life, for introducing the concepts of the right to the city and the production of social space, and for his work on dialectics, alienation, and criticism of Stalinism and structuralism. In his prolific career, Lefebvre wrote more than sixty books and three hundred articles. Biography In 1961, Lefebvre became professor of sociology at the University of Strasbourg, before joining the faculty at the new university at Nanterre in 1965. He was one of the most respected professors, and he had influenced and analysed the May 1968 students revolt. Lefebvre introduced the concept of the right to the city in his 1968 book Le Droit à la ville (the publication of the book predates the May 1968 revolts which took place in many French cities). Lefebvre died in 1991. The critique of everyday life "Change life!
Bayesian gameIn game theory, a Bayesian game is one in which information about characteristics of the other players (i.e. payoffs) is incomplete. Following John C. Harsanyi's framework, a Bayesian game can be modelled by introducing Nature as a player in a game. Nature assigns a random variable to each player which could take values of types for each player and associating probabilities or a probability density function with those types (in the course of the game, nature randomly chooses a type for each player according to the probability distribution across each player's type space). Such games are called Bayesian because of the probabilistic analysis inherent in the game. Specification of games The normal form representation of a non-Bayesian game with perfect information is a specification of the strategy spaces and payoff functions of players. In a Bayesian game, it is to specify the strategy spaces, type spaces, payoff functions and beliefs for every player. ). , where The pure strategy