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Bayesian-optimal Pricing
Bayesian-optimal pricing (BO pricing) is a kind of algorithmic pricing in which a seller determines the sell-prices based on probabilistic assumptions on the valuations of the buyers. It is a simple kind of a Bayesian-optimal mechanism, in which the price is determined in advance without collecting actual buyers' bids. Single item and single buyer In the simplest setting, the seller has a single item to sell (with zero cost), and there is a single potential buyer. The highest price that the buyer is willing to pay for the item is called the ''valuation'' of the buyer. The seller would like to set the price exactly at the buyer's valuation. Unfortunately, the seller does not know the buyer's valuation. In the Bayesian model, it is assumed that the buyer's valuation is a random variable drawn from a known probability distribution. Suppose the cumulative distribution function of the buyer is F(v), defined as the probability that the seller's valuation is less than v. Then, if the pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmic Pricing
Algorithmic pricing is the practice of automatically setting the requested price for items for sale, in order to maximize the seller's profits. Dynamic pricing algorithms usually rely on one or more of the following data. * Probabilistic and statistical information on potential buyers; see Bayesian-optimal pricing. * Prices of competitors. E.g., a seller of an item may automatically detect the lowest price currently offered for that item, and suggest a price within $1 of that price. * Personal information of the currently active buyer, such as her or his demographics and her or his interest in the product. If the seller detects that you are about to buy, your price goes up. * Business information of the seller, such as the expected date in which he or she is going to receive new stocks, or her or his target selling velocity in units per day. See also * Algorithmic trading * Contribution margin * Price optimization software * Pricing * Tacit collusion * Yield management Yield m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Matroid
In mathematics, a uniform matroid is a matroid in which the independent sets are exactly the sets containing at most ''r'' elements, for some fixed integer ''r''. An alternative definition is that every permutation of the elements is a symmetry. Definition The uniform matroid U^r_n is defined over a set of n elements. A subset of the elements is independent if and only if it contains at most r elements. A subset is a basis if it has exactly r elements, and it is a circuit if it has exactly r+1 elements. The rank of a subset S is \min(, S, ,r) and the rank of the matroid is r. A matroid of rank r is uniform if and only if all of its circuits have exactly r+1 elements. The matroid U^2_n is called the n-point line. Duality and minors The dual matroid of the uniform matroid U^r_n is another uniform matroid U^_n. A uniform matroid is self-dual if and only if r=n/2. Every minor of a uniform matroid is uniform. Restricting a uniform matroid U^r_n by one element (as long as r 0) prod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monopoly Pricing
A monopoly price is set by a monopoly.Roger LeRoy Miller, ''Intermediate Microeconomics Theory Issues Applications, Third Edition'', New York: McGraw-Hill, Inc, 1982.Tirole, Jean, "The Theory of Industrial Organization", Cambridge, Massachusetts: The MIT Press, 1988. A monopoly occurs when a firm lacks any viable competition and is the sole producer of the industry's product. Because a monopoly faces no competition, it has absolute market power and can set a price above the firm's marginal cost. Since marginal cost is the increment in total cost required to produce an additional unit of the product, the firm can make a positive economic profit if it produces a greater quantity of the product and sells it at a lower price. The monopoly ensures a monopoly price exists when it establishes the quantity of the product. As the sole supplier of the product within the market, its sales establish the entire industry's supply within the market, and the monopoly's production and sales decisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Auction
A double auction is a process of buying and selling goods with multiple sellers and multiple buyers. Potential buyers submit their bids and potential sellers submit their ask prices to the market institution, and then the market institution chooses some price ''p'' that clears the market: all the sellers who asked less than ''p'' sell and all buyers who bid more than ''p'' buy at this price ''p''. Buyers and sellers that bid or ask for exactly ''p'' are also included. A common example of a double auction is stock exchange. As well as their direct interest, double auctions are reminiscent of Walrasian auction and have been used as a tool to study the determination of prices in ordinary markets. A double auction is also possible without any exchange of currency in barter trade. A barter double auction is an auction where every participant has a demand and an offer consisting of multiple attributes and no money is involved. For the mathematical modelling of satisfaction level Euclid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truthful Mechanism
In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information about what the others do, you fare best or at least not worse by being truthful. SP is also called truthful or dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. An SP game is not always immune to collusion, but its robust variants are; with group strategyproofness no group of people can collude to misreport their preferences in a way that makes every member better off, and with strong group strategyproofness no group of people can collude to misreport their preferences in a way that makes at least one member of the group better off without making any of the remaining members worse off. Examples Typical examples of SP mechanisms are majority voting between two alternatives, second- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
With High Probability
In mathematics, an event that occurs with high probability (often shortened to w.h.p. or WHP) is one whose probability depends on a certain number ''n'' and goes to 1 as ''n'' goes to infinity, i.e. the probability of the event occurring can be made as close to 1 as desired by making ''n'' big enough. Applications The term WHP is especially used in computer science, in the analysis of probabilistic algorithms. For example, consider a certain probabilistic algorithm on a graph with ''n'' nodes. If the probability that the algorithm returns the correct answer is 1-1/n, then when the number of nodes is very large, the algorithm is correct with a probability that is very near 1. This fact is expressed shortly by saying that the algorithm is correct WHP. Some examples where this term is used are: * Miller–Rabin primality test: a probabilistic algorithm for testing whether a given number ''n'' is prime or composite. If ''n'' is composite, the test will detect ''n'' as composite WHP. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation Gap
In stochastic programming, the correlation gap is the worst-case ratio between the cost when the random variables are correlated to the cost when the random variables are independent. As an example, consider the following optimization problem. A teacher wants to know whether to come to class or not. There are ''n'' potential students. For each student, there is a probability of 1/''n'' that the student will attend the class. If at least one student attends, then the teacher must come and his cost is 1. If no students attend, then the teacher can stay at home and his cost is 0. The goal of the teacher is to minimize his cost. This is a stochastic-programming problem, because the constraints are not known in advance – only their probabilities are known. Now, there are two cases regarding the correlation between the students: * Case #1: the students are uncorrelated: each student decides whether to come to class or not by tossing a coin with probability 1/n, independently o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matroid Rank
In the mathematical theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset ''S'' of elements of the matroid is, similarly, the maximum size of an independent subset of ''S'', and the rank function of the matroid maps sets of elements to their ranks. The rank function is one of the fundamental concepts of matroid theory via which matroids may be axiomatized. Matroid rank functions form an important subclass of the submodular set functions. The rank functions of matroids defined from certain other types of mathematical object such as undirected graphs, matrices, and field extensions are important within the study of those objects. Examples In all examples, ''E'' is the base set of the matroid, and ''B'' is some subset of ''E''. * Let ''M'' be the free matroid, where the independent sets are all subsets of ''E''. Then the rank function of ''M'' is simply: ''r''(''B'') = , ''B'', . * Let ''M'' be a uniform matroid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphic Matroid
In the mathematical theory of matroids, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the forests in a given finite undirected graph. The dual matroids of graphic matroids are called co-graphic matroids or bond matroids. A matroid that is both graphic and co-graphic is sometimes called a planar matroid (but this should not be confused with matroids of rank 3, which generalize planar point configurations); these are exactly the graphic matroids formed from planar graphs. Definition A matroid may be defined as a family of finite sets (called the "independent sets" of the matroid) that is closed under subsets and that satisfies the "exchange property": if sets A and B are both independent, and A is larger than B, then there is an element x\in A\setminus B such that B\cup\ remains independent. If G is an undirected graph, and F is the family of sets of edges that form forests in G, then F is clearly closed under subsets (re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Matroid
In mathematics, a partition matroid or partitional matroid is a matroid that is a direct sum of uniform matroids. It is defined over a base set in which the elements are partitioned into different categories. For each category, there is a ''capacity constraint'' - a maximum number of allowed elements from this category. The independent sets of a partition matroid are exactly the sets in which, for each category, the number of elements from this category is at most the category capacity. Formal definition Let C_i be a collection of disjoint sets ("categories"). Let d_i be integers with 0\le d_i\le , C_i, ("capacities"). Define a subset I\subset \bigcup_i C_i to be "independent" when, for every index i, , I\cap C_i, \le d_i. The sets satisfying this condition form the independent sets of a matroid, called a partition matroid. The sets C_i are called the categories or the blocks of the partition matroid. A basis of the partition matroid is a set whose intersection with every bloc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shuchi Chawla
Shuchi Chawla is an Indian computer scientist who works in the design and analysis of algorithms, and is known for her research on correlation clustering, information privacy, mechanism design, approximation algorithms, hardness of approximation, and algorithmic bias. She works as a professor of computer science at the University of Texas at Austin. Education and career Chawla earned a bachelor's degree from the Indian Institute of Technology Delhi in 2000, and received her Ph.D. from Carnegie Mellon University in 2005. Her dissertation, ''Graph Algorithms for Planning and Partitioning'', was supervised by Avrim Blum. After postdoctoral studies at Stanford University under the mentorship of Tim Roughgarden, and at Microsoft Research, Silicon Valley, she joined the Wisconsin faculty in 2006.. She joined the UT-Austin faculty in 2021. She won a Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian-optimal Mechanism
A Bayesian-optimal mechanism (BOM) is a mechanism in which the designer does not know the valuations of the agents for whom the mechanism is designed, but the designer knows that they are random variables and knows the probability distribution of these variables. A typical application is a seller who wants to sell some items to potential buyers. The seller wants to price the items in a way that will maximize their profit. The optimal prices depend on the amount that each buyer is willing to pay for each item. The seller does not know these amounts, but assumes that they are drawn from a certain known probability distribution. The phrase "Bayesian optimal mechanism design" has the following meaning: * Bayesian means that we know the probability distribution from which the agents' valuations are drawn (in contrast to prior-free mechanism design, which do not assume any prior probability distribution). * Optimal means that we want to maximize the expected revenue of the auctioneer, wher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
