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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 satisfies 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. It is assumed that ... [...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. The five axioms, any Nash Bargaining Solution should satisfy are Pareto Optimality (PAR), Individual Rationality (IR), Independent of Expected Utility Representations (INV), Independence of Irrelevant Alternatives (IIA) ... [...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 (1972–75), 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 direc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Irrelevant Alternatives
The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used in different connotation in several contexts. Although it always attempts to provide an account of rational individual behavior or aggregation of individual preferences, the exact formulation differs widely in both language and exact content. Perhaps the easiest way to understand the axiom is how it pertains to casting a ballot. There the axiom says that if Charlie (the irrelevant alternative) enters a race between Alice and Bob, with Alice (leader) liked better than Bob (runner-up), then the individual voter who likes Charlie less than Alice will not switch his vote from Alice to Bob. Because of this, a violation of IIA is commonly referred to as the "spoiler effect": support for Charlie "spoils" the election for Alice, while it "logically" should not have. After all, Alice ''was'' liked better ... [...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
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. 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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and natu ... [...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 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence Of Irrelevant Alternatives
The independence of irrelevant alternatives (IIA), also known as binary independence or the independence axiom, is an axiom of decision theory and various social sciences. The term is used in different connotation in several contexts. Although it always attempts to provide an account of rational individual behavior or aggregation of individual preferences, the exact formulation differs widely in both language and exact content. Perhaps the easiest way to understand the axiom is how it pertains to casting a ballot. There the axiom says that if Charlie (the irrelevant alternative) enters a race between Alice and Bob, with Alice (leader) liked better than Bob (runner-up), then the individual voter who likes Charlie less than Alice will not switch his vote from Alice to Bob. Because of this, a violation of IIA is commonly referred to as the "spoiler effect": support for Charlie "spoils" the election for Alice, while it "logically" should not have. After all, Alice ''was'' liked better ... [...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 among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game 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 mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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