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Revenue Equivalence
Revenue equivalence is a concept in auction theory that states that given certain conditions, any mechanism that results in the same outcomes (i.e. allocates items to the same bidders) also has the same expected revenue. Notation There is a set X of possible outcomes. There are n agents which have different valuations for each outcome. The valuation of agent i (also called its "type") is represented as a function: : v_i : X \longrightarrow R_ which expresses the value it has for each alternative, in monetary terms. The agents have quasilinear utility functions; this means that, if the outcome is x and in addition the agent receives a payment p_i (positive or negative), then the total utility of agent i is: : u_i := v_i(x) + p_i The vector of all value-functions is denoted by v. For every agent i, the vector of all value-functions of the ''other'' agents is denoted by v_. So v \equiv (v_i,v_). A ''mechanism'' is a pair of functions: * An Outcome function, that takes as inpu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Auction Theory
Auction theory is a branch of applied economics that deals with how bidders act in auctions and researches how the features of auctions Incentivisation, incentivise predictable outcomes. Auction theory is a tool used to inform the design of real-world auctions. Sellers use auction theory to raise higher revenues while allowing buyers to procure at a lower cost. The confluence of the price between the buyer and seller is an economic equilibrium. Auction theorists design rules for auctions to address issues that can lead to market failure. The design of these rulesets encourages optimal bidding strategies in a variety of informational settings. The 2020 Nobel Prize for Economics was awarded to Paul R. Milgrom and Robert B. Wilson "for improvements to auction theory and inventions of new Auction#Types, auction formats." Introduction Auctions facilitate transactions by enforcing a specific set of rules regarding the resource allocations of a group of bidders. Theorists consider auctio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-price Sealed-bid Auction
A first-price sealed-bid auction (FPSBA) is a common type of auction. It is also known as blind auction. In this type of auction, all bidders simultaneously submit sealed bids so that no bidder knows the bid of any other participant. The highest bidder pays the price that was submitted. Strategic analysis In a FPSBA, each bidder is characterized by their monetary valuation of the item for sale. Suppose Alice is a bidder and her valuation is a. Then, if Alice is rational: *She will never bid more than a, because bidding more than a can only make her lose net value. *If she bids exactly a, then she will not lose but also not gain any positive value. *If she bids less than a, then she ''may'' have some positive gain, but the exact gain depends on the bids of the others. Alice would like to bid the smallest amount that can make her win the item, as long as this amount is less than a. For example, if there is another bidder Bob and he bids y and y [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Winner's Curse
The winner's curse is a phenomenon that may occur in common value auctions, where all bidders have the same (''ex post'') value for an item but receive different private (''ex ante'') signals about this value and wherein the winner is the bidder with the most optimistic evaluation of the asset and therefore will tend to overestimate and overpay. Accordingly, the winner will be "cursed" in one of two ways: either the winning bid will exceed the value of the auctioned asset making the winner worse off in absolute terms, or the value of the asset will be less than the bidder anticipated, so the bidder may garner a net gain but will be worse off than anticipated. However, an actual overpayment will generally occur only if the winner fails to account for the winner's curse when bidding (an outcome that, according to the revenue equivalence theorem, need never occur). The winner’s curse phenomenon was first addressed in 1971 by three Atlantic Richfield petroleum engineers who claim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk Aversion
In economics and finance, risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter is equal to or higher in monetary value than the more certain outcome. Risk aversion explains the inclination to agree to a situation with a lower average payoff that is more predictable rather than another situation with a less predictable payoff that is higher on average. For example, a risk-averse investor might choose to put their money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value. Example A person is given the choice between two scenarios: one with a guaranteed payoff, and one with a risky payoff with same average value. In the former scenario, the person receives $50. In the uncertain scenario, a coin is flipped to decide whether the person receives $100 or nothing. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reservation Price
In economics, a reservation (or reserve) price is a limit on the price of a good (economics), good or a service (economics), service. On the demand side, it is the highest price that a buyer is Willingness to pay, willing to pay; on the supply (economics), supply side, it is the lowest price a seller is Willingness to accept, willing to accept for a good or service. Reservation prices are commonly used in auctions, but the concept can be extended beyond. A party's best alternative to a negotiated agreement (BATNA), is closely related to their reservation price. Once a party determines their BATNA, they can further calculate their reservation price. In negotiations surrounding the price of a particular good or service, the reservation price is a singular number. However, this is not the only situation where reservation prices are seen. When multiple issues are being discussed, such as the size of salary and amount of Employee benefits, benefits when applying for a new job position, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Distribution (continuous)
In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, a and b, which are the minimum and maximum values. The interval can either be closed (i.e. ,b/math>) or open (i.e. (a,b)). Therefore, the distribution is often abbreviated U(a,b), where U stands for uniform distribution. The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable X under no constraint other than that it is contained in the distribution's support. Definitions Probability density function The probability density function of the continuous uniform distribution is f(x) = \begin \dfrac & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Auction
An English auction is an open-outcry ascending dynamic auction. It proceeds as follows. * The auctioneer opens the auction by announcing a suggested opening bid, a starting price, or a reserve for the item on sale. * Then the auctioneer accepts increasingly higher bids from the floor and sometimes from other sources, for example online or telephone bids. The auctioneer usually determines the minimum increment of bids, often making them larger as bidding reaches higher levels. * The highest bidder at any given moment is considered to have the standing bid, which can only be displaced by a higher bid from a competing buyer. * If no competing bidder challenges the standing bid within the time allowed by the auctioneer, the standing bid becomes the winner, and the item is sold to the highest bidder at a price equal to their bid. *If no bidder accepts the starting price, the auctioneer either begins to lower the starting price in increments, or bidders are allowed to bid prices lowe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vickrey Auction
A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest bid. This type of auction is strategically similar to an English auction and gives bidders an incentive to bid their true value. The auction was first described academically by Columbia University professor William Vickrey in 1961 though it had been used by stamp collectors since 1893. In 1797 Johann Wolfgang von Goethe sold a manuscript using a sealed-bid, second-price auction. Vickrey's original paper mainly considered auctions where only a single, indivisible good is being sold. The terms ''Vickrey auction'' and ''second-price sealed-bid auction'' are, in this case only, equivalent and used interchangeably. In the case of multiple identical goods, the bidders submit inverse demand curves and pay the opportunity cost. Vickrey auctio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
All-pay Auction
In economics and game theory, an all-pay auction is an auction in which every bidder must pay regardless of whether they win the prize, which is awarded to the highest bidder as in a conventional auction. As shown by Riley and Samuelson (1981), equilibrium bidding in an all pay auction with private information is revenue equivalent to bidding in a sealed high bid or open ascending price auction. In the simplest version, there is complete information. The Nash equilibrium is such that each bidder plays a mixed strategy and expected pay-offs are zero.Jehiel P, Moldovanu B (2006) Allocative and informational externalities in auctions and related mechanisms. In: Blundell R, Newey WK, Persson T (eds) Advances in Economics and Econometrics: Volume 1: Theory and Applications, Ninth World Congress, vol 1, Cambridge University Press, chap 3 The seller's expected revenue is equal to the value of the prize. However, some economic experiments and studies have shown that over-bidding is common ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Price Auction
A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest bid. This type of auction is strategically similar to an English auction and gives bidders an incentive to bid their true value. The auction was first described academically by Columbia University professor William Vickrey in 1961 though it had been used by stamp collectors since 1893. In 1797 Johann Wolfgang von Goethe sold a manuscript using a sealed-bid, second-price auction. Vickrey's original paper mainly considered auctions where only a single, indivisible good is being sold. The terms ''Vickrey auction'' and ''second-price sealed-bid auction'' are, in this case only, equivalent and used interchangeably. In the case of multiple identical goods, the bidders submit inverse demand curves and pay the opportunity cost. Vickrey auctions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasilinear Utility
In economics and consumer theory, quasilinear utility functions are linear in one argument, generally the numeraire. Quasilinear preferences can be represented by the utility function u ( x,y_1,..,y_n ) = x + \theta_1(y_1)+..+\theta_n(y_n) where \theta_i is strictly increasing and concave. A useful property of the quasilinear utility function is that the Marshallian/Walrasian demand for y_1, \ldots, y_n does not depend on wealth and is thus not subject to a wealth effect; The absence of a wealth effect simplifies analysis and makes quasilinear utility functions a common choice for modelling. Furthermore, when utility is quasilinear, compensating variation (CV), equivalent variation (EV), and consumer surplus are algebraically equivalent. In mechanism design, quasilinear utility ensures that agents can compensate each other with side payments. Definition in terms of preferences A preference relation \succsim is quasilinear with respect to commodity 1 (called, in this case, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Price Auction
A first-price sealed-bid auction (FPSBA) is a common type of auction. It is also known as blind auction. In this type of auction, all bidders simultaneously submit sealed bids so that no bidder knows the bid of any other participant. The highest bidder pays the price that was submitted. Strategic analysis In a FPSBA, each bidder is characterized by their monetary valuation of the item for sale. Suppose Alice is a bidder and her valuation is a. Then, if Alice is rational: *She will never bid more than a, because bidding more than a can only make her lose net value. *If she bids exactly a, then she will not lose but also not gain any positive value. *If she bids less than a, then she ''may'' have some positive gain, but the exact gain depends on the bids of the others. Alice would like to bid the smallest amount that can make her win the item, as long as this amount is less than a. For example, if there is another bidder Bob and he bids y and y [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
