|
Fair Division
Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth observation satellites. It is an active research area in mathematics, economics (especially social choice theory), dispute resolution, etc. The central tenet of fair division is that such a division should be performed by the players themselves, maybe using a mediator but certainly not an arbiter as only the players really know how they value the goods. The archetypal fair division algorithm is divide and choose. It demonstrates that two agents with different tastes can divide a cake such that each of them believes that he got the best piece. The research in fair division can be seen as an exten ... [...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 mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Cake-cutting
Fair cake-cutting is a kind of fair division problem. The problem involves a ''heterogeneous'' resource, such as a cake with different toppings, that is assumed to be ''divisible'' – it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e., some people prefer the chocolate toppings, some prefer the cherries, some just want as large a piece as possible. The division should be ''unanimously'' fair - each person should receive a piece that he or she believes to be a fair share. The "cake" is only a metaphor; procedures for fair cake-cutting can be used to divide various kinds of resources, such as land estates, advertisement space or broadcast time. The prototypical procedure for fair cake-cutting is divide and choose, which is mentioned already in the book of Genesis. It solves the fair division problem for two people. The modern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envy-free
Envy-freeness, also known as no-envy, is a criterion for fair division. It says that, when resources are allocated among people with equal rights, each person should receive a share that is, in their eyes, at least as good as the share received by any other agent. In other words, no person should feel envy. General definitions Suppose a certain resource is divided among several agents, such that every agent i receives a share X_i. Every agent i has a personal preference relation \succeq_i over different possible shares. The division is called envy-free (EF) if for all i and j: :::X_i \succeq_i X_j Another term for envy-freeness is no-envy (NE). If the preference of the agents are represented by a value functions V_i, then this definition is equivalent to: :::V_i(X_i) \geq V_i(X_j) Put another way: we say that agent i ''envies'' agent j if i prefers the piece of j over his own piece, i.e.: :::X_i \prec_i X_j :::V_i(X_i) 2 the problem is much harder. See envy-free cake-cutting. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Super-proportional Division
A strongly-proportional division (sometimes called super-proportional division) is a kind of a fair division. It is a division of resources among ''n'' partners, in which the value received by each partner is strictly more than his/her due share of 1/''n'' of the total value. Formally, in a strongly-proportional division of a resource ''C'' among ''n'' partners, each partner ''i'', with value measure ''Vi'', receives a share ''Xi'' such thatV_i(X_i) > V_i(C)/n.Obviously, a strongly-proportional division does not exist when all partners have the same value measure. The best condition that can ''always'' be guaranteed is V_i(X_i) \geq V_i(C)/n, which is the condition for a plain proportional division. However, one may hope that, when different agents have different valuations, it may be possible to use this fact for the benefit of all players, and give each of them strictly more than their due share. Existence In 1948, Hugo Steinhaus conjectured the existence of a super-proportiona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportional Division
A proportional division is a kind of fair division in which a resource is divided among ''n'' partners with subjective valuations, giving each partner at least 1/''n'' of the resource by his/her own subjective valuation. Proportionality was the first fairness criterion studied in the literature; hence it is sometimes called "simple fair division". It was first conceived by Steinhaus. Example Consider a land asset that has to be divided among 3 heirs: Alice and Bob who think that it's worth 3 million dollars, and George who thinks that it's worth $4.5M. In a proportional division, Alice receives a land-plot that she believes to be worth at least $1M, Bob receives a land-plot that ''he'' believes to be worth at least $1M (even though Alice may think it is worth less), and George receives a land-plot that he believes to be worth at least $1.5M. Existence A proportional division does not always exist. For example, if the resource contains several indivisible items and the number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alice And Bob
Alice and Bob are fictional characters commonly used as placeholders in discussions about cryptographic systems and protocols, and in other science and engineering literature where there are several participants in a thought experiment. The Alice and Bob characters were invented 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 to aid comprehension. For example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subjective Theory Of Value
The subjective theory of value is an economic theory which proposes the idea that the value of any good is not determined by the utility value of the object, nor by the cumulative value of components or labour needed to produce or manufacture it, but instead is determined by the individuals or entities who are buying or selling the object in question. This trend is often seen in collectable items such as cars, vinyl records, and comic books. The value of an object may have increased substantially since its creation or original purchase due to age, a personal affinity, or scarcity. The modern version of this theory was created independently and nearly simultaneously by William Stanley Jevons, Léon Walras, and Carl Menger in the late 19th century.Stigler, George (1950) "The Development of Utility Theory. I" ''The Journal of Political Economy'' Overview According to the subjective theory of value, by assuming that all trades between individuals are voluntary, it can be concluded tha ... [...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, and the term ''bankruptcy'' is therefore not a synonym for insolvency. Etymology The word ''bankruptcy'' is derived from Italian ''banca rotta'', literally meaning "broken bank". 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 so that the public could see that the banker, the owner of the bench, was no longer in a condition to continue his business, although some dismiss this as a false etymology. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entitlement (fair Division)
Entitlement in fair division describes that proportion of the resources or goods to be divided that a player can expect to receive. In many fair division settings, all agents have ''equal entitlements'', which means that each agent is entitled to 1/''n'' of the resource. But there are practical settings in which agents have ''different entitlements''. Some examples are: * In partnership resolution settings, each partner is entitled to a fraction of the common assets in proportion to his/her investment in the partnership. * In inheritance settings, the law in some jurisdictions prescribes a different share to each heir according to his/her proximity to the deceased person. For example, according to the Bible, the firstborn son must receive twice as much as every other son. In contrast, according to the Italian law, when there are three heirs - parent, brother and spouse - they are entitled to 1/4, 1/12 and 2/3 respectively. * In parliamentary democracies, each party is entitled to a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Talmud
The Talmud (; he, , Talmūḏ) is the central text of Rabbinic Judaism and the primary source of Jewish religious law (''halakha'') and Jewish theology. Until the advent of modernity, in nearly all Jewish communities, the Talmud was the centerpiece of Jewish cultural life and was foundational to "all Jewish thought and aspirations", serving also as "the guide for the daily life" of Jews. The term ''Talmud'' normally refers to the collection of writings named specifically the Babylonian Talmud (), although there is also an earlier collection known as the Jerusalem Talmud (). It may also traditionally be called (), a Hebrew abbreviation of , or the "six orders" of the Mishnah. The Talmud has two components: the Mishnah (, 200 CE), a written compendium of the Oral Torah; and the Gemara (, 500 CE), an elucidation of the Mishnah and related Tannaitic writings that often ventures onto other subjects and expounds broadly on the Hebrew Bible. The term "Talmud" may refer to eith ... [...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 ''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 Tribes o ... [...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, sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Fair Cake-cutting")
.png "Click for more on -> Bankrupt")
