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No-justified-envy Matching
In economics and social choice theory, a no-justified-envy matching is a matching in a two-sided market, in which no agent prefers the assignment of another agent and is simultaneously preferred by that assignment. Consider, for example, the task of matching doctors for residency in hospitals. Each doctor has a preference relation on hospitals, ranking the hospitals from best to worst. Each hospital has a preference relation on doctors, ranking the doctors from best to worst. Each doctor can work in at most one hospital, and each hospital can employ at most a fixed number of doctors (called the ''capacity'' of the hospital). The goal is to match doctors to hospitals, without monetary transfers. ''Envy'' is a situation in which some doctor ''d''1, employed in some hospital ''h''1, prefers some other hospital ''h''2, which employs some other doctor ''d''2 (we say that ''d1 envies d2''). The envy is ''justified'' if, at the same time, ''h''2 prefers ''d''1 over ''d''2. Note that, if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economics
Economics () is the social science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyzes the economy as a system where production, consumption, saving, and investment interact, and factors affecting it: employment of the resources of labour, capital, and land, currency inflation, economic growth, and public policies that have impact on glossary of economics, these elements. Other broad distinctions within economics include those between positive economics, desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Choice Theory
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a ''collective decision'' or ''social welfare'' in some sense.Amartya Sen (2008). "Social Choice,". ''The New Palgrave Dictionary of Economics'', 2nd EditionAbstract & TOC./ref> Whereas choice theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with how to translate the preferences of individuals into the preferences of a group. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Another example is voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences. Social choice blends elements of welfare economics and public choice theory. It is methodologically individualistic, in that it aggregates preferences and behaviors of individual member ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-sided Market
A two-sided market, also called a two-sided network, is an intermediary economic platform having two distinct user groups that provide each other with network benefits. The organization that creates value primarily by enabling direct interactions between two (or more) distinct types of affiliated customers is called a multi-sided platform. This concept of two-sided markets has been mainly theorised by the French economists Jean Tirole and Jean-Charles Rochet and Americans Geoffrey G Parker and Marshall Van Alstyne. Two-sided networks can be found in many industries, sharing the space with traditional product and service offerings. Example markets include credit cards (composed of cardholders and merchants); health maintenance organizations (patients and doctors); operating systems (end-users and developers); yellow pages (advertisers and consumers); video-game consoles (gamers and game developers); recruitment sites (job seekers and recruiters); search engines (advertisers and us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residency (medicine)
Residency or postgraduate training is specifically a stage of graduate medical education. It refers to a qualified physician (one who holds the degree of MD, DO, MBBS, MBChB), veterinarian ( DVM or VMD) , dentist ( DDS or DMD) or podiatrist ( DPM) who practices medicine, veterinary medicine , dentistry, or podiatry, respectively, usually in a hospital or clinic, under the direct or indirect supervision of a senior medical clinician registered in that specialty such as an attending physician or consultant. In many jurisdictions, successful completion of such training is a requirement in order to obtain an unrestricted license to practice medicine, and in particular a license to practice a chosen specialty. In the meantime they practice "on" the license of their supervising physician. An individual engaged in such training may be referred to as a resident, registrar or trainee depending on the jurisdiction. Residency training may be followed by fellowship or sub-specialty trai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Preference (economics)
In economics and other social sciences, preference is the order that an agent gives to alternatives based on their relative utility. A process which results in an "optimal choice" (whether real or theoretical). Preferences are evaluations and concern matters of value, typically in relation to practical reasoning. The character of the preferences is determined purely by a person's tastes instead of the good's prices, personal income, and the availability of goods. However, people are still expected to act in their best (rational) interest. Rationality, in this context, means that when individuals are faced with a choice, they would select the option that maximizes self-interest. Moreover, in every set of alternatives, preferences arise. The belief of preference plays a key role in many disciplines, including moral philosophy and decision theory. The logical properties that preferences possess have major effects also on rational choice theory, which has a carryover effect on all mode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envy-free Matching
In economics and social choice theory, an envy-free matching (EFM) is a matching between people to "things", which is envy-free in the sense that no person would like to switch his "thing" with that of another person. This term has been used in several different contexts. In unweighted bipartite graphs In an unweighted bipartite graph G = (''X''+''Y'', ''E''), an envy-free matching is a matching in which no unmatched vertex in ''X'' is adjacent to a matched vertex in ''Y''. Suppose the vertices of ''X'' represent people, the vertices of ''Y'' represent houses, and an edge between a person ''x'' and a house ''y'' represents the fact that ''x'' is willing to live in ''y''. Then, an EFM is a partial allocation of houses to people such that each house-less person does not envy any person with a house, since he/she does not like any allocated house anyway. Every matching that saturates ''X'' is envy-free, and every empty matching is envy-free. Moreover, if , ''NG''(''X''), ≥ , X ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stable Matching
In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is ''not'' stable if: In other words, a matching is stable when there does not exist any pair (''A'', ''B'') which both prefer each other to their current partner under the matching. The stable marriage problem has been stated as follows: The existence of two classes that need to be paired with each other (heterosexual men and women in this example) distinguishes this problem from the stable roommates problem. Applications Algorithms for finding solutions to the stable marriage problem have applications in a variety of real-world situations, perhaps the best known of these being in the assignment of graduating medical student ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gale–Shapley Algorithm
In mathematics, economics, and computer science, the Gale–Shapley algorithm (also known as the deferred acceptance algorithm or propose-and-reject algorithm) is an algorithm for finding a solution to the stable matching problem, named for David Gale and Lloyd Shapley. It takes polynomial time, and the time is linear in the size of the input to the algorithm. It is a truthful mechanism from the point of view of the proposing participants, for whom the solution will always be optimal. Background The stable matching problem, in its most basic form, takes as input equal numbers of two types of participants ( medical students and internships, for example), and an ordering for each participant giving their preference for whom to be matched to among the participants of the other type. A stable matching always exists, and the algorithmic problem solved by the Gale–Shapley algorithm is to find one. A matching is ''not'' stable if: In other words, a matching is stable when there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These ''lattice-like'' structures all admi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fixed Point (mathematics)
A fixed point (sometimes shortened to fixpoint, also known as an invariant point) is a value that does not change under a given transformation. Specifically, in mathematics, a fixed point of a function is an element that is mapped to itself by the function. In physics, the term fixed point can refer to a temperature that can be used as a reproducible reference point, usually defined by a phase change or triple point. Fixed point of a function Formally, is a fixed point of a function if belongs to both the domain and the codomain of , and . For example, if is defined on the real numbers by f(x) = x^2 - 3 x + 4, then 2 is a fixed point of , because . Not all functions have fixed points: for example, , has no fixed points, since is never equal to for any real number. In graphical terms, a fixed point means the point is on the line , or in other words the graph of has a point in common with that line. Fixed-point iteration In numerical analysis, ''fixed-point iter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tarsky Operator , Russia
{{Disambiguation, geo ...
Tarsky (masculine), Tarskaya (feminine), or Tarskoye (neuter) may refer to: *Tarsky District, a district of Omsk Oblast, Russia *Alfred Tarski (1901–1983), Polish logician and mathematician * Tarsky (rural locality), a rural locality (a ''khutor'') in Stavropol Krai, Russia * Tarskaya, a rural locality (a settlement at the station) in Zabaykalsky Krai, Russia * Tarskoye, a rural locality (a ''selo'') in the Republic of North Ossetia–Alania A republic () is a "state in which power rests with the people or their representatives; specifically a state without a monarchy" and also a "government, or system of government, of such a state." Previously, especially in the 17th and 18th c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rural Hospitals Theorem
The rural hospitals theorem (RHT) is a fundamental theorem in the theory of stable matching. It considers the problem of matching doctors to hospitals for residency, where each doctor is matched to a single hospital but each hospital has several positions for doctors. The total number of positions is larger than the total number of doctors, so some hospitals inevitably remain with unfilled positions. Usually, ''rural hospitals'' are less wanted than urban hospitals, so they often remain with many empty positions. This raised the question of whether the mechanism used to match doctors to hospitals can be changed in order to help these rural hospitals. The ''rural hospitals theorem'' answers this question negatively assuming all preferences are strict (i.e., no doctor is indifferent between two hospitals and no hospital is indifferent between two doctors). The theorem has two parts: # The set of assigned doctors, and the number of filled positions in each hospital, are the same in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
