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Sequential Auction
A sequential auction is an auction in which several items are sold, one after the other, to the same group of potential buyers. In a ''sequential first-price auction'' (SAFP), each individual item is sold using a first price auction, while in a ''sequential second-price auction'' (SASP), each individual item is sold using a second price auction. A sequential auction differs from a combinatorial auction, in which many items are auctioned simultaneously and the agents can bid on bundles of items. A sequential auction is much simpler to implement and more common in practice. However, the bidders in each auction know that there are going to be future auctions, and this may affect their strategic considerations. Here are some examples. Example 1. There are two items for sale and two potential buyers: Alice and Bob, with the following valuations: * Alice values each item as 5, and both items as 10 (i.e., her valuation is additive). * Bob values each item as 4, and both items as 4 (i.e., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Auction
An auction is usually a process of buying and selling goods or services by offering them up for bids, taking bids, and then selling the item to the highest bidder or buying the item from the lowest bidder. Some exceptions to this definition exist and are described in the section about different types. The branch of economic theory dealing with auction types and participants' behavior in auctions is called auction theory. The open ascending price auction is arguably the most common form of auction and has been used throughout history. Participants bid openly against one another, with each subsequent bid being higher than the previous bid. An auctioneer may announce prices, while bidders submit bids vocally or electronically. Auctions are applied for trade in diverse contexts. These contexts include antiques, paintings, rare collectibles, expensive wines, commodities, livestock, radio spectrum, used cars, real estate, online advertising, vacation packages, emission trading, ... [...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) implie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Nash Equilibrium
In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the solutions to games with incomplete information. Hungarian economist John C. Harsanyi introduced the concept of Bayesian games in three papers from 1967 and 1968: He was awarded the Nobel Prize for these and other contributions to game theory in 1994. Roughly speaking, Harsanyi defined Bayesian games in the following way: players are assigned by nature at the start of the game a set of characteristics. By mapping probability distributions to these characteristics and by calculating the outcome of the game using Bayesian probability, the result is a game whose solution is, for technical reasons, far easier to calculate than a similar game in a non-Bayesian context. For those technical reasons, see the Specification of games section in this articl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Game
In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the solutions to games with incomplete information. Hungarian economist John C. Harsanyi introduced the concept of Bayesian games in three papers from 1967 and 1968: He was awarded the Nobel Prize for these and other contributions to game theory in 1994. Roughly speaking, Harsanyi defined Bayesian games in the following way: players are assigned by nature at the start of the game a set of characteristics. By mapping probability distributions to these characteristics and by calculating the outcome of the game using Bayesian probability, the result is a game whose solution is, for technical reasons, far easier to calculate than a similar game in a non-Bayesian context. For those technical reasons, see the Specification of games section in this artic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gross Substitute Valuation
The term gross substitutes is used in two slightly different meanings: # In microeconomics, two commodities X and Y are called gross substitutes, if \frac > 0. I.e., an increase in the price of one commodity causes people to want ''strictly more'' of the other commodity, since the commodities can substitute each other (bus and taxi are a common example). # In auction theory and competitive equilibrium theory, a valuation function is said to have the ''gross substitutes'' (GS) property if for all pairs of commodities: \frac\geq 0. I.e., the definition includes both substitute goods and independent goods, and only rules out complementary goods. See Gross substitutes (indivisible items) In economics, gross substitutes (GS) is a class of utility functions on indivisible goods. An agent is said to ''have a GS valuation'' if, whenever the prices of some items increase and the prices of other items remain constant, the agent's demand .... References {{Econ-term-stub Utility func ... [...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 ... [...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] |
Independent Goods
Independent goods are goods that have a zero cross elasticity of demand. Changes in the price of one good will have no effect on the demand for an independent good. Thus independent goods are neither complements nor substitutes. For example, a person's demand for nails is usually independent of his or her demand for bread, since they are two unrelated types of goods. Note that this concept is subjective and depends on the consumer's personal utility function. A Cobb-Douglas utility function implies that goods are independent. For goods in quantities ''X''1 and ''X''2, prices ''p''1 and ''p''2, income ''m'', and utility function parameter ''a'', the utility function : u(X_1, X_2) = X_1^a X_2^, when optimized subject to the budget constraint that expenditure on the two goods cannot exceed income, gives rise to this demand function for good 1: X_1= am/p_1, which does not depend on ''p''2. See also * Consumer theory * Good (economics and accounting) In economics, goods are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diminishing Returns
In economics, diminishing returns are the decrease in marginal (incremental) output of a production process as the amount of a single factor of production is incrementally increased, holding all other factors of production equal ( ceteris paribus). The law of diminishing returns (also known as the law of diminishing marginal productivity) states that in productive processes, increasing a factor of production by one unit, while holding all other production factors constant, will at some point return a lower unit of output per incremental unit of input. The law of diminishing returns does not cause a decrease in overall production capabilities, rather it defines a point on a production curve whereby producing an additional unit of output will result in a loss and is known as negative returns. Under diminishing returns, output remains positive, however productivity and efficiency decrease. The modern understanding of the law adds the dimension of holding other outputs equal, since ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Information
In economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions (including risk aversion), payoffs, strategies and "types" of players are thus common knowledge. Complete information is the concept that each player in the game is aware of the sequence, strategies, and payoffs throughout gameplay. Given this information, the players have the ability to plan accordingly based on the information to maximize their own strategies and utility at the end of the game. Inversely, in a game with incomplete information, players do not possess full information about their opponents. Some players possess private information, a fact that the others should take into account when forming expectations about how those players will behave. A typical example is an auction: each player knows his own utility function (valuation for the item), but does not know the utili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Of Anarchy
The Price of Anarchy (PoA) is a concept in economics and game theory that measures how the efficiency of a system degrades due to selfish behavior of its agents. It is a general notion that can be extended to diverse systems and notions of efficiency. For example, consider the system of transportation of a city and many agents trying to go from some initial location to a destination. Let efficiency in this case mean the average time for an agent to reach the destination. In the 'centralized' solution, a central authority can tell each agent which path to take in order to minimize the average travel time. In the 'decentralized' version, each agent chooses its own path. The Price of Anarchy measures the ratio between average travel time in the two cases. Usually the system is modeled as a game and the efficiency is some function of the outcomes (e.g. maximum delay in a network, congestion in a transportation system, social welfare in an auction, etc.). Different concepts of equilib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
