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Kalai–Smorodinsky Bargaining Solution
The Kalai–Smorodinsky (KS) bargaining solution is a solution to the Bargaining problem. It was suggested by Ehud Kalai and Meir Smorodinsky, as an alternative to Nash's bargaining solution suggested 25 years earlier. The main difference between the two solutions is that the Nash solution satisfies independence of irrelevant alternatives, while the KS solution instead satisfies resource monotonicity. Setting A two-person bargain problem consists of a pair (F,d): * A feasible agreements set F. This is a closed convex subset of \mathbb^2. Each element of F represents a possible agreement between the players. The coordinates of an agreement are the utilities of the players if this agreement is implemented. The assumption that F is convex makes sense, for example, when it is possible to combine agreements by randomization. * A disagreement point d=(d_1, d_2), where d_1 and d_2 are the respective payoffs to player 1 and player 2 when the bargaining terminates without an agreement. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bargaining Problem
Cooperative bargaining is a process in which two people decide how to share a surplus that they can jointly generate. In many cases, the surplus created by the two players can be shared in many ways, forcing the players to negotiate which division of payoffs to choose. Such surplus-sharing problems (also called bargaining problem) are faced by management and labor in the division of a firm's profit, by trade partners in the specification of the terms of trade, and more. The present article focuses on the ''normative'' approach to bargaining. It studies how the surplus ''should'' be shared, by formulating appealing axioms that the solution to a bargaining problem should satisfy. It is useful when both parties are willing to cooperate in implementing the fair solution. Such solutions, particularly the Nash solution, were used to solve concrete economic problems, such as management–labor conflicts, on numerous occasions. An alternative approach to bargaining is the ''positive'' appr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehud Kalai
Ehud Kalai () is a prominent Israeli American game theorist and mathematical economist known for his contributions to the field of game theory and its interface with economics, social choice, computer science and operations research. He was the James J. O’Connor Distinguished Professor of Decision and Game Sciences at Northwestern University, 1975–2017 and currently is a Professor Emeritus of Managerial Economics and Decision Sciences. Biography Born in Mandatory Palestine on December 7, 1942, Kalai moved to the US in 1963. He received his AB in mathematics from the University of California Berkeley (1967) and an MS (1971) and a PhD (1972) in statistics and mathematics from Cornell University. After serving as an assistant professor of statistics at Tel Aviv University (1972–1975), he was hired by Northwestern University to establish a research group in game theory. He is the founding director of the Kellogg Center of Game Theory and Economic Behavior and the executive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Irrelevant Alternatives
Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between A and B (which are both related) should not depend on the quality of a third, unrelated outcome C. There are several different variations of this axiom, which are generally equivalent under mild conditions. As a result of its importance, the axiom has been independently rediscovered in various forms across a wide variety of fields, including economics, cognitive science, social choice, fair division, rational choice, artificial intelligence, probability, and game theory. It is closely tied to many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski–Young theorem, and the money pump arguments. In behavioral economics, failures of IIA (caused by irrationality) are called menu effects or menu dependence. Motivation This is sometimes explained with a short story by philosopher Sidney Morgenbesser:Mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resource Monotonicity
Resource monotonicity (RM; aka aggregate monotonicity) is a principle of fair division. It says that, if there are more resources to share, then all agents should be weakly better off; no agent should lose from the increase in resources. The RM principle has been studied in various division problems. Allocating divisible resources Single homogeneous resource, general utilities Suppose society has m units of some homogeneous divisible resource, such as water or flour. The resource should be divided among n agents with different utilities. The utility of agent i is represented by a function u_i; when agent i receives y_i units of resource, he derives from it a utility of u_i(y_i). Society has to decide how to divide the resource among the agents, i.e, to find a vector y_1,\dots,y_n such that: y_1+\cdots+y_n = m. Two classic allocation rules are the egalitarian rule - aiming to equalize the utilities of all agents (equivalently: maximize the minimum utility), and the utilitari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pareto Optimality
In welfare economics, a Pareto improvement formalizes the idea of an outcome being "better in every possible way". A change is called a Pareto improvement if it leaves at least one person in society better off without leaving anyone else worse off than they were before. A situation is called Pareto efficient or Pareto optimal if all possible Pareto improvements have already been made; in other words, there are no longer any ways left to make one person better off without making some other person worse-off. In social choice theory, the same concept is sometimes called the unanimity principle, which says that if ''everyone'' in a society ( non-strictly) prefers A to B, society as a whole also non-strictly prefers A to B. The Pareto front consists of all Pareto-efficient situations. 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 go ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry (social Choice)
In economics and social choice, a function satisfies anonymity, neutrality, or symmetry if the rule does not discriminate between different participants ahead of time. For example, in an election, a voter-anonymous function is one where it does not matter who casts which vote, i.e. all voters' ballots are equal ahead of time. Formally, this is defined by saying the rule returns the same outcome (whatever this may be) if the votes are "relabeled" arbitrarily, e.g. by swapping votes #1 and #2. Similarly, outcome-neutrality says the rule does not discriminate between different outcomes (e.g. candidates) ahead of time. Formally, if the labels assigned to each outcome are permuted arbitrarily, the returned result is permuted in the same way. Some authors reserve the term anonymity for agent symmetry and neutrality for outcome-symmetry, but this pattern is not perfectly consistent.{{Rp, 75 Examples Most voting rules are anonymous and neutral by design. For example, plurality voting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affine Transformation
In Euclidean geometry, an affine transformation or affinity (from the Latin, '' affinis'', "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments. Consequently, sets of parallel affine subspaces remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line. If is the point set of an affine space, then every affine transformation on can ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Irrelevant Alternatives
Independence of irrelevant alternatives (IIA) is an axiom of decision theory which codifies the intuition that a choice between A and B (which are both related) should not depend on the quality of a third, unrelated outcome C. There are several different variations of this axiom, which are generally equivalent under mild conditions. As a result of its importance, the axiom has been independently rediscovered in various forms across a wide variety of fields, including economics, cognitive science, social choice, fair division, rational choice, artificial intelligence, probability, and game theory. It is closely tied to many of the most important theorems in these fields, including Arrow's impossibility theorem, the Balinski–Young theorem, and the money pump arguments. In behavioral economics, failures of IIA (caused by irrationality) are called menu effects or menu dependence. Motivation This is sometimes explained with a short story by philosopher Sidney Morgenbesser:Mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resource Monotonicity
Resource monotonicity (RM; aka aggregate monotonicity) is a principle of fair division. It says that, if there are more resources to share, then all agents should be weakly better off; no agent should lose from the increase in resources. The RM principle has been studied in various division problems. Allocating divisible resources Single homogeneous resource, general utilities Suppose society has m units of some homogeneous divisible resource, such as water or flour. The resource should be divided among n agents with different utilities. The utility of agent i is represented by a function u_i; when agent i receives y_i units of resource, he derives from it a utility of u_i(y_i). Society has to decide how to divide the resource among the agents, i.e, to find a vector y_1,\dots,y_n such that: y_1+\cdots+y_n = m. Two classic allocation rules are the egalitarian rule - aiming to equalize the utilities of all agents (equivalently: maximize the minimum utility), and the utilitari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
