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Shapley–Shubik Power Index
The Shapley–Shubik power index was formulated by Lloyd Shapley and Martin Shubik in 1954 to measure the powers of players in a voting game. The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players in an ''n''-player game. Players with the same preferences form coalitions. Any coalition that has enough votes to pass a bill or elect a candidate is called winning. The power of a coalition (or a player) is measured by the fraction of the possible voting sequences in which that coalition casts the deciding vote, that is, the vote that first guarantees passage or failure. The power index is normalized between 0 and 1. A power of 0 means that a coalition has no effect at all on the outcome of the game; and a power of 1 means a coalition determines the outcome by its vote. Also the sum of the powers of all the players is always equal to 1. There are some algorithms for calculating the power ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lloyd Shapley
Lloyd Stowell Shapley (; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Memorial Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of the most important contributors to the development of game theory since the work of von Neumann and Morgenstern. With Alvin E. Roth, Shapley won the 2012 Nobel Memorial Prize in Economic Sciences "for the theory of stable allocations and the practice of market design." Life and career Lloyd Shapley was born on June 2, 1923, in Cambridge, Massachusetts, one of the sons of astronomers Harlow Shapley and Martha Betz Shapley, both from Missouri. He attended Phillips Exeter Academy and was a student at Harvard when he was drafted in 1943. He served in the United States Army Air Corps in Chengdu, China and received the Bronze Star decoration for breaking the Soviet weather code. After the war, Shapley returned to Harvard and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Shubik
Martin Shubik (1926–2018) was an American mathematical economist who specialized in game theory, defense analysis, and the theory of money. The latter was his main research interest and he referred to it as his "white whale". He also coined the term "mathematical institutional economics" in 1959 to describe his scholarly approach to studying the economy. He spent the majority of his career at Yale University Yale University is a Private university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ..., where he was heavily involved with the Cowles Foundation for Research in Economics, and launched the virtuaMuseum of Money and Financial Institutions Outside of economics, he began studying inclusion body myositis (IBM) after a 2003 diagnosis. He provided seed money to the Yale School of Public Health for thIBM Disease Reg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-player Game
In game theory, an ''n''-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players. In defining ''n''-player games, game theorists usually provide a definition that allow for any (finite) number of players. The limiting case of n \to \infty is the subject of mean field game theory. Changing games from 2-player games to ''n''-player games entails some concerns. For instance, the Prisoner's dilemma is a 2-player game. One might define an ''n''-player Prisoner's Dilemma where a single defection results everyone else getting the sucker's payoff. Alternatively, it might take certain amount of defection before the cooperators receive the sucker's payoff. (One example of an ''n''-player Prisoner's Dilemma is the Diner's dilemma.) Analysis ''n''-player games can not be solved using minimax Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial
In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \times (n-3) \times \cdots \times 3 \times 2 \times 1 \\ &= n\times(n-1)!\\ \end For example, 5! = 5\times 4! = 5 \times 4 \times 3 \times 2 \times 1 = 120. The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book ''Sefer Yetzirah''. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there In mathematical analysis, factorials are used in power series for the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Council Of The European Union
The Council of the European Union, often referred to in the treaties and other official documents simply as the Council, and less formally known as the Council of Ministers, is the third of the seven institutions of the European Union (EU) as listed in the Treaty on European Union. It is one of two legislative bodies and together with the European Parliament serves to amend and approve, or veto, the proposals of the European Commission, which holds the right of initiative. The Council of the European Union and the European Council are the only EU institutions that are explicitly intergovernmental, that is, forums whose attendees express and represent the position of their Member State's executive, be they ambassadors, ministers or heads of state/government. The Council meets in 10 different configurations of national ministers (one per state). The precise membership of these configurations varies according to the topic under consideration; for example, when discussin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United Nations Security Council
The United Nations Security Council (UNSC) is one of the six principal organs of the United Nations (UN) and is charged with ensuring international peace and security, recommending the admission of new UN members to the General Assembly, and approving any changes to the UN Charter. Its powers as outlined in the United Nations Charter include establishing peacekeeping operations, enacting international sanctions, and authorizing military action. The UNSC is the only UN body with authority to issue resolutions that are binding on member states. Like the UN as a whole, the Security Council was created after World War II to address the failings of the League of Nations in maintaining world peace. It held its first session on 17 January 1946 but was largely paralysed in the following decades by the Cold War between the United States and the Soviet Union (and their allies). Nevertheless, it authorized military interventions in the Korean War and the Congo Crisis and peaceke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shapley Value
In cooperative game theory, the Shapley value is a method (solution concept) for fairly distributing the total gains or costs among a group of players who have collaborated. For example, in a team project where each member contributed differently, the Shapley value provides a way to determine how much credit or blame each member deserves. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 2012. The Shapley value determines each player's contribution by considering how much the overall outcome changes when they join each possible combination of other players, and then averaging those changes. In essence, it calculates each player's average marginal contribution across all possible coalitions. It is the only solution that satisfies four fundamental properties: efficiency, symmetry, additivity, and the dummy player (or null player) property, which are widely accepted as defining a fair distribution. This m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrow Theorem
Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational choice. Specifically, Arrow showed no such rule can satisfy the independence of irrelevant alternatives axiom. This is the principle that a choice between two alternatives and should not depend on the quality of some third, unrelated option, . The result is often cited in discussions of voting rules, where it shows no ranked voting rule to eliminate the spoiler effect. This result was first shown by the Marquis de Condorcet, whose voting paradox showed the impossibility of logically-consistent majority rule; Arrow's theorem generalizes Condorcet's findings to include non-majoritarian rules like collective leadership or consensus decision-making. While the impossibility theorem shows all ranked voting rules must have spoilers, the frequency of spoilers differs dramatically by rule. Plurality-rule fami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banzhaf Power Index
The Banzhaf power index, named after John Banzhaf (originally invented by Lionel Penrose in 1946 and sometimes called Penrose–Banzhaf index; also known as the Banzhaf–Coleman index after James Samuel Coleman), is a power index defined by the probability of changing an outcome of a vote where voting rights are not necessarily equally divided among the voters or shareholders. To calculate the power of a voter using the Banzhaf index, list all the winning coalitions, then count the critical voters. A ''critical voter'' is a voter who, if he changed his vote from yes to no, would cause the measure to fail. A voter's power is measured as the fraction of all swing votes that he could cast. There are some algorithms for calculating the power index, e.g., dynamic programming techniques, enumeration methods and Monte Carlo methods. Examples Voting game Simple voting game A simple voting game, taken from ''Game Theory and Strategy'' by Philip D. Straffin: ; 4, 3, 2, 1 The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC (programming language), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and Data and information visualization, data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of R package, software packages, which contain Reusability, reusable code, documentation, and sample data. Some of the most popular R packages are in the tidyverse collection, which enhances functionality for visualizing, transforming, and modelling data, as well as improves the ease of programming (according to the authors and users). R is free and open-source software distributed under the GNU General Public License. The language is implemented primarily in C (programming language), C, Fortran, and Self-hosting (compilers), R itself. Preprocessor, Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a na ... [...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] |
