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Contested Garment Rule
The contested garment (CG) rule, also called concede-and-divide, is a division rule for solving problems of conflicting claims (also called "bankruptcy problems"). The idea is that, if one claimant's claim is less than 100% of the estate to divide, then he effectively ''concedes'' the unclaimed estate to the other claimant. Therefore, we first give to each claimant, the amount conceded to him/her by the other claimant. The remaining amount is then divided equally among the two claimants. The CG rule first appeared in the Mishnah, exemplified by a case of conflict over a garment, hence the name. In the Mishnah, it was described only for two-people problems. But in 1985, Robert Aumann and Michael Maschler have proved that, in every bankruptcy problem, there is a unique division that is consistent with the CG rule for each pair of claimants. They call the rule, that selects this unique division, the CG-consistent rule (it is also called the Talmud rule). Problem description There i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bankruptcy Problem
A bankruptcy problem, also called a claims problem, is a problem of distributing a homogeneous divisible good (such as money) among people with different claims. The focus is on the case where the amount is insufficient to satisfy all the claims. The canonical application is a bankrupt firm that is to be liquidated. The firm owes different amounts of money to different creditors, but the total worth of the company's assets is smaller than its total debt. The problem is how to divide the scarce existing money among the creditors. Another application would be the division of an estate amongst several heirs, particularly when the estate cannot meet all the deceased's commitments. A third application is ''tax assessment''. One can consider the claimants as taxpayers, the claims as the incomes, and the endowment as the total after-tax income. Determining the allocation of total after-tax income is equivalent to determining the allocation of tax payments. Definitions The amount ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mishnah
The Mishnah or the Mishna (; he, מִשְׁנָה, "study by repetition", from the verb ''shanah'' , or "to study and review", also "secondary") is the first major written collection of the Jewish oral traditions which is known as the Oral Torah. It is also the first major work of rabbinic literature. The Mishnah was redacted by Judah ha-Nasi probably in Beit Shearim or Sepphoris at the beginning of the 3rd century CE in a time when, according to the Talmud, the persecution of the Jews and the passage of time raised the possibility that the details of the oral traditions of the Pharisees from the Second Temple period (516 BCE – 70 CE) would be forgotten. Most of the Mishnah is written in Mishnaic Hebrew, but some parts are in Aramaic. The Mishnah consists of six orders (', singular ' ), each containing 7–12 tractates (', singular ' ; lit. "web"), 63 in total, and further subdivided into chapters and paragraphs. The word ''Mishnah'' can also indicate a single paragraph of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Aumann
Robert John Aumann (Hebrew name: , Yisrael Aumann; born June 8, 1930) is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel. He also holds a visiting position at Stony Brook University, and is one of the founding members of the Stony Brook Center for Game Theory. Aumann received the Nobel Memorial Prize in Economic Sciences in 2005 for his work on conflict and cooperation through game theory analysis. He shared the prize with Thomas Schelling. Early years Aumann was born in Frankfurt am Main, Germany, and fled to the United States with his family in 1938, two weeks before the Kristallnacht pogrom. He attended the Rabbi Jacob Joseph School, a yeshiva high school in New York City. Academic career Aumann graduated from the City College of New York in 1950 with a B.Sc. in mathematics. He received his M.Sc. in 1952, and his Ph.D. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Maschler
Michael Bahir Maschler (Hebrew: ) (July 22, 1927 – July 20, 2008) was an Israeli mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ... well known for his contributions to the field of game theory. He was a professor in the Einstein Institute of Mathematics and the Center for the Study of Rationality at the Hebrew University of Jerusalem in Israel. In 2012, the Israeli Chapter of the Game Theory Society founded the Maschler Prize, an annual prize awarded to an outstanding research student in game theory and related topics in Israel. Biography Michael B. Maschler was born in Jerusalem on July 22, 1927. Selected publications For a complete list of English and Hebrew publications, see Michael Maschler: In Memoriam, above. * "The Bargaining Set for Cooperative Gam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherence (fairness)
Coherence, also called uniformity or consistency, is a criterion for evaluating rules for fair division. Coherence requires that the outcome of a fairness rule is fair not only for the overall problem, but also for each sub-problem. Every part of a fair division should be fair. The coherence requirement was first studied in the context of apportionment. In this context, failure to satisfy coherence is called the new states paradox: when a new state enters the union, and the house size is enlarged to accommodate the number of seats allocated to this new state, some other unrelated states are affected. Coherence is also relevant to other fair division problems, such as bankruptcy problems. Definition There is a ''resource'' to allocate, denoted by h. For example, it can be an integer representing the number of seats in a ''h''ouse of representatives. The resource should be allocated between some n ''agents''. For example, these can be federal states or political parties. The agent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bava Metzia
Bava Metzia (Talmudic Aramaic: בָּבָא מְצִיעָא, "The Middle Gate") is the second of the first three Talmudic tractates in the order of Nezikin ("Damages"), the other two being Bava Kamma and Bava Batra. Originally all three formed a single tractate called ''Nezikin'' (torts or injuries), each ''Bava'' being a Part or subdivision. Bava Metzia discusses civil matters such as property law and usury. It also examines one's obligations to guard lost property that have been found, or property explicitly entrusted to him. Mishnah The Mishnah of Bava Metzia contains ten chapters. Honorary trustee (''Shomer Hinam''), chapters 1-3 An honorary trustee is one who finds lost property. He has to keep it as '' shomer hinam'' (watching over another's property without receiving any remuneration) until he can restore it to the rightful owner (). The laws as to what constitutes finding, what to do with the things found, how to guard against false claimants, how to take care of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constrained Equal Awards
Constrained equal awards (CEA), also called constrained equal gains, is a division rule for solving bankruptcy problems. According to this rule, each claimant should receive an equal amount, except that no claimant should receive more than his/her claim. In the context of taxation, it is known as leveling tax. Formal definition There is a certain amount of money to divide, denoted by ''E'' (=Estate or Endowment). There are ''n'' ''claimants''. Each claimant ''i'' has a ''claim'' denoted by ''c_i''. Usually, \sum_^n c_i > E, that is, the estate is insufficient to satisfy all the claims. The CEA rule says that each claimant ''i'' should receive \min(c_i, r), where ''r'' is a constant chosen such that \sum_^n \min(c_i,r) = E. The rule can also be described algorithmically as follows: * Initially, all agents are active, and all agents get 0. * While there are remaining units of the estate: ** The next estate unit is divided equally among all active agents. ** Each agent whose tot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constrained Equal Losses
Constrained equal losses (CEL) is a division rule for solving bankruptcy problems. According to this rule, each claimant should lose an equal amount from his or her claim, except that no claimant should receive a negative amount. In the context of taxation, it is known as poll tax. Formal definition There is a certain amount of money to divide, denoted by ''E'' (=Estate or Endowment). There are ''n'' ''claimants''. Each claimant ''i'' has a ''claim'' denoted by ''c_i''. Usually, \sum_^n c_i > E, that is, the estate is insufficient to satisfy all the claims. The CEL rule says that each claimant ''i'' should receive \max(0, c_i-r), where ''r'' is a constant chosen such that \sum_^n \max(0, c_i-r) = E. The rule can also be described algorithmically as follows: * Initially, all agents are active, and each agent gets his full claim. * While the total allocation is larger than the estate: ** Remove one unit equally from all active agents. ** Each agent whose total allocation dr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ketubot (tractate)
Ketubot ( he, כְּתוּבּוׂת) is a tractate of the Mishnah and the Talmud in the order of Nashim. It deals with a variety of marital responsibilities, especially those intended for the marital contract, also named the ''ketubah''. Due to the wide breadth of subjects discussed in this tractate, Ketubot is often referred to as the ''Shas katan (the miniature Talmud)''. A ketubah (plural: ketubot) (in Hebrew: כְּתוּבָּה; plural: כְּתוּבּוׂת) is a special type of Jewish prenuptial agreement. It is considered an integral part of a traditional Jewish marriage, and describes the groom's rights and responsibilities towards the bride. Currently, the ketubah does not have a monetary value, however, it has legal value in Israel. " Broyde, Michael and Jonathan Reiss. Journal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooperative Game Theory
In game theory, a cooperative game (or coalitional game) is a game with competition between groups of Player (game), players ("coalitions") due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be Self-enforcing agreement, self-enforcing (e.g. through credible threats). Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional Non-cooperative game, non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steven Landsburg
Steven E. Landsburg (born February 24, 1954) is an American professor of economics at the University of Rochester in Rochester, New York. From 1989 to 1995, he taught at Colorado State University. Landsburg is also an outspoken commentator on economic, legal, and political issues whose comments have sometimes been regarded as controversial. Education Landsburg was an undergraduate at the University of Rochester. Landsburg received a PhD in mathematics from the University of Chicago in 1979. Writings and work Commentary and opinions Landsburg wrote a column on "everyday economics" for ''Slate'' magazine from 1996 to 2008. The subjects of the columns were diverse and often drew on current affairs. In them, Landsburg discussed the national debt, the obesity crisis, payments to Hurricane Katrina evacuees in New Orleans and salary caps in the NFL. Landsburg also discussed recent research in micro-economics and its implications, as in an article on the value of mobile phones and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
