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Fair Division
Fair division is the problem in game theory of dividing a set of resources among several people who have an Entitlement (fair division), entitlement to them so that each person receives their due share. The central tenet of fair division is that such a division should be performed by the players themselves, without the need for external arbitration, as only the players themselves really know how they value the goods. There are many different kinds of fair division problems, depending on the nature of goods to divide, the criteria for fairness, the nature of the players and their preferences, and other criteria for evaluating the quality of the division. The archetypal fair division algorithm is divide and choose. The research in fair division can be seen as an extension of this procedure to various more complex settings. Description In game theory, fair division is the problem of dividing a set of resources among several people who have an Entitlement (fair division), entitlem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cake Cutting Division
Cake is a Flour confections, flour confection usually made from flour, sugar, and other ingredients and is usually baking, baked. In their oldest forms, cakes were modifications of bread, but cakes now cover a wide range of preparations that can be simple or elaborate and which share features with Dessert, desserts such as pastry, pastries, meringues, custards, and pies. The most common ingredients include flour, sugar, eggs, fat (such as butter, Vegetable oil, oil, or margarine), a liquid, and a leavening agent, such as baking soda or baking powder. Common additional ingredients include Dried fruit, dried, candied fruit, candied, or fresh fruit, nut (fruit), nuts, cocoa powder, cocoa, and extracts such as vanilla, with numerous substitutions for the primary ingredients. Cakes can also be filled with fruit preserves, nuts, or dessert sauces (like custard, Fruit preserves, jelly, cooked fruit, whipped cream, or syrups), iced with buttercream or other Icing (food), icings, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Disk
In mathematics, the open unit disk (or disc) around ''P'' (where ''P'' is a given point in the plane), is the set of points whose distance from ''P'' is less than 1: :D_1(P) = \.\, The closed unit disk around ''P'' is the set of points whose distance from ''P'' is less than or equal to one: :\bar D_1(P)=\.\, Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself. Without further specifications, the term ''unit disk'' is used for the open unit disk about the origin, D_1(0), with respect to the standard Euclidean metric. It is the interior of a circle of radius 1, centered at the origin. This set can be identified with the set of all complex numbers of absolute value less than one. When viewed as a subset of the complex plane (C), the unit disk is often denoted \mathbb. The open unit disk, the plane, and the upper half-plane The function :f(z)=\frac is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alice And Bob
Alice and Bob are fictional characters commonly used as placeholders in discussions about cryptography, cryptographic systems and Cryptographic protocol, protocols, and in other science and engineering literature where there are several participants in a thought experiment. The Alice and Bob characters were created by Ron Rivest, Adi Shamir, and Leonard Adleman in their 1978 paper "A Method for Obtaining Digital Signatures and Public-key Cryptosystems". Subsequently, they have become common archetypes in many scientific and engineering fields, such as quantum cryptography, game theory and physics. As the use of Alice and Bob became more widespread, additional characters were added, sometimes each with a particular meaning. These characters do not have to refer to people; they refer to generic agents which might be different computers or even different programs running on a single computer. Overview Alice and Bob are the names of fictional characters used for convenience and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subjective Theory Of Value
The subjective theory of value (STV) is an theory of value (economics), economic theory for explaining how the value of goods and services are not only set but also how they can fluctuate over time. The contrasting system is typically known as the labor theory of value. STV's development helped to better understand human action and decision making in economics. The theory claims that the value (economics), value of a good is not determined by any inherent property of the good, nor by the cumulative value of components or labor needed to produce it, but instead is determined by the individuals or entities who are buying (and/or selling) that good. Thus a good's value may increase substantially following its creation if the good is perceived as being of greater importance, or as being more desirable than before. There are many variables that can influence this process, including, but not limited to, changes in the age of the good, personal affinity, cultural significance, scarcity, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bankrupt
Bankruptcy is a legal process through which people or other entities who cannot repay debts to creditors may seek relief from some or all of their debts. In most jurisdictions, bankruptcy is imposed by a court order, often initiated by the debtor. Bankrupt is not the only legal status that an insolvent person may have, meaning the term ''bankruptcy'' is not a synonym for insolvency. Etymology The word ''bankruptcy'' is derived from Italian , literally meaning . The term is often described as having originated in Renaissance Italy, where there allegedly existed the tradition of smashing a banker's bench if he defaulted on payment. However, the existence of such a ritual is doubted. History In Ancient Greece, bankruptcy did not exist. If a man owed and he could not pay, he and his wife, children or servants were forced into " debt slavery" until the creditor recouped losses through their physical labour. Many city-states in ancient Greece limited debt slavery to a perio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entitlement (fair Division)
In fair division, a person's entitlement is the value of the goods they are owed or deserve, i.e. the total value of the goods or resources that a player would ideally receive. For example, in party-list proportional representation, a party's seat entitlement (sometimes called its seat quota) is equal to its share of the vote, times the number of seats in the legislature. Dividing money Even when only money is to be divided and some fixed amount has been specified for each recipient, the problem can be complex. The amounts specified may be more or less than the amount of money, and the profit or loss will then need to be shared out. The proportional rule is normally used in law nowadays, and is the default assumption in the theory of bankruptcy. However, other rules can also be used. For example: * The Shapley value is one common method of deciding bargaining power, as can be seen in the airport problem. * Welfare economics on the other hand tries to determine allocations de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Talmud
The Talmud (; ) is the central text of Rabbinic Judaism and the primary source of Jewish religious law (''halakha'') and Jewish theology. Until the advent of Haskalah#Effects, modernity, in nearly all Jewish communities, the Talmud was the centerpiece of Jewish culture, Jewish cultural life and was foundational to "all Jewish thought and aspirations", serving also as "the guide for the daily life" of Jews. The Talmud includes the teachings and opinions of thousands of rabbis on a variety of subjects, including halakha, Jewish ethics, Jewish philosophy, philosophy, Jewish customs, customs, Jewish history, history, and Jewish folklore, folklore, and many other topics. The Talmud is a commentary on the Mishnah. This text is made up of 63 Masekhet, tractates, each covering one subject area. The language of the Talmud is Jewish Babylonian Aramaic. Talmudic tradition emerged and was compiled between the destruction of the Second Temple in 70 CE and the Arab conquest in the early seve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Random Assignment
Fair random assignment (also called probabilistic one-sided matching) is a kind of a fair division problem. In an ''assignment problem'' (also called '' house-allocation problem'' or '' one-sided matching''), there are ''m'' objects and they have to be allocated among ''n'' agents, such that each agent receives at most one object. Examples include the assignment of jobs to workers, rooms to housemates, dormitories to students, time-slots to users of a common machine, and so on. In general, a fair assignment may be impossible to attain. For example, if Alice and Batya both prefer the eastern room to the western room, only one of them will get it and the other will be envious. In the random assignment setting, fairness is attained using a lottery. So in the simple example above, Alice and Batya will toss a fair coin and the winner will get the eastern room. History Random assignment is mentioned already in the Bible: a lottery was used to allocate the lands of Canaan among the Tri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair River Sharing
Fair river sharing is a kind of a fair division problem in which the waters of a river has to be divided among countries located along the river. It differs from other fair division problems in that the resource to be divided—the water—flows in one direction—from upstream countries to downstream countries. To attain any desired division, it may be required to limit the consumption of upstream countries, but this may require to give these countries some monetary compensation. In addition to sharing river water, which is an economic good, it is often required to share river pollution (or the cost of cleaning it), which is an economic bad. River sharing in practice There are 148 rivers in the world flowing through two countries, 30 through three, nine through four and 13 through five or more. Some notable examples are: * The Jordan River, whose sources run from upstream Lebanon and Syria to downstream Israel and Jordan. The attempts of Syria to divert the Jordan River, star ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Housemates Problem
Rental harmony is a kind of a fair division problem in which indivisible items and a fixed monetary cost have to be divided simultaneously. The housemates problem and room-assignment-rent-division are alternative names to the same problem. In the typical setting, there are n partners who rent together an n-room house for cost fixed by the homeowner. Each housemate may have different preferences — one may prefer a large room, another may prefer a room with a view to the main road, etc. The following two problems should be solved simultaneously: * (a) Assign a room to each partner, * (b) Determine the amount each partner should pay, such that the sum of payments equals the fixed cost. There are several properties that we would like the assignment to satisfy. * Non-negativity (NN): all prices must be 0 or more: no partner should be paid to get a room. * Envy-freeness (EF): Given a pricing scheme (an assignment of rent to rooms), we say that a partner ''prefers'' a given room if h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chore Division
Chore division is a fair division problem in which the divided resource is undesirable, so that each participant wants to get as little as possible. It is the mirror-image of the fair cake-cutting problem, in which the divided resource is desirable so that each participant wants to get as much as possible. Both problems have heterogeneous resources, meaning that the resources are nonuniform. In cake division, cakes can have edge, corner, and middle pieces along with different amounts of frosting. Whereas in chore division, there are different chore types and different amounts of time needed to finish each chore. Similarly, both problems assume that the resources are divisible. Chores can be infinitely divisible, because the finite set of chores can be partitioned by chore or by time. For example, a load of laundry could be partitioned by the number of articles of clothing and/or by the amount of time spent loading the machine. The problems differ, however, in the desirability of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Pie-cutting
The fair pie-cutting problem is a variation of the fair cake-cutting problem, in which the resource to be divided is circular. As an example, consider a birthday cake shaped as a disk. The cake should be divided among several children such that no child envies another child (as in a standard cake-cutting problem), with the additional constraint that the cuts must be radial, so that each child receives a circular sector. A possible application of the pie model might be for dividing an island’s shoreline into connected lots. Another possible application is in division of periodic time, such as dividing a daily cycle into "on-call" periods. Model A pie is usually modeled as the 1-dimensional interval ,2π(or ,1, in which the two endpoints are identified. This model was introduced in 1985 and later in 1993. Every procedure for fair cake-cutting can also be applied to cutting a pie by just ignoring the fact that the two endpoints are identified. For example, if the cake-cutti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
