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Unit Demand
In economics, a unit demand agent is an agent who wants to buy a single item, which may be of one of different types. A typical example is a buyer who needs a new car. There are many different types of cars, but usually a buyer will choose only one of them, based on the quality and the price. If there are ''m'' different item-types, then a unit-demand valuation function is typically represented by ''m'' values v_1,\dots,v_m, with v_j representing the subjective value that the agent derives from item j. If the agent receives a set A of items, then his total utility is given by: :u(A)=\max_v_j since he enjoys the most valuable item from A and ignores the rest. Therefore, if the price of item j is p_j, then a unit-demand buyer will typically want to buy a single item – the item j for which the net utility v_j - p_j is maximized. Ordinal and cardinal definitions A unit-demand valuation is formally defined by: * For a preference relation: for every set B there is a subset A\subsete ... [...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] |
Submodular Set Function
In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the difference in the incremental value of the function that a single element makes when added to an input set decreases as the size of the input set increases. Submodular functions have a natural diminishing returns property which makes them suitable for many applications, including approximation algorithms, game theory (as functions modeling user preferences) and electrical networks. Recently, submodular functions have also found immense utility in several real world problems in machine learning and artificial intelligence, including automatic summarization, multi-document summarization, feature selection, active learning, sensor placement, image collection summarization and many other domains. Definition If \Omega is a finite set, a submodular function is a set function f:2^\rightarrow \mathbb, where 2^\Omega denotes the power set of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substitute Goods
In microeconomics, two goods are substitutes if the products could be used for the same purpose by the consumers. That is, a consumer perceives both goods as similar or comparable, so that having more of one good causes the consumer to desire less of the other good. Contrary to complementary goods and independent goods, substitute goods may replace each other in use due to changing economic conditions. An example of substitute goods is Coca-Cola and Pepsi; the interchangeable aspect of these goods is due to the similarity of the purpose they serve, i.e fulfilling customers' desire for a soft drink. These types of substitutes can be referred to as close substitutes. Definition Economic theory describes two goods as being close substitutes if three conditions hold: # products have the same or similar performance characteristics # products have the same or similar occasion for use and # products are sold in the same geographic area Performance characteristics describe what the pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Utility Functions On Indivisible Goods
Some branches of economics and game theory deal with indivisible goods, discrete items that can be traded only as a whole. For example, in combinatorial auctions there is a finite set of items, and every agent can buy a subset of the items, but an item cannot be divided among two or more agents. It is usually assumed that every agent assigns subjective utility to every subset of the items. This can be represented in one of two ways: * An ordinal utility preference relation, usually marked by \succ. The fact that an agent prefers a set A to a set B is written A \succ B. If the agent only weakly prefers A (i.e. either prefers A or is indifferent between A and B) then this is written A \succeq B. * A cardinal utility function, usually denoted by u. The utility an agent gets from a set A is written u(A). Cardinal utility functions are often normalized such that u(\emptyset)=0, where \emptyset is the empty set. A cardinal utility function implies a preference relation: u(A)>u(B) implies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matching (graph Theory)
In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. Finding a matching in a bipartite graph can be treated as a network flow problem. Definitions Given a graph a matching ''M'' in ''G'' is a set of pairwise non-adjacent edges, none of which are loops; that is, no two edges share common vertices. A vertex is matched (or saturated) if it is an endpoint of one of the edges in the matching. Otherwise the vertex is unmatched (or unsaturated). A maximal matching is a matching ''M'' of a graph ''G'' that is not a subset of any other matching. A matching ''M'' of a graph ''G'' is maximal if every edge in ''G'' has a non-empty intersection with at least one edge in ''M''. The following figure shows examples of maximal matchings (red) in three graphs. : A maximum matching (also known as maximum-cardinality matching) is a matching that contains the largest possible number of edges. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
