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Encyclopedia > Winner's curse

The winner's curse is a phenomenon akin to a Pyrrhic victory that occurs in common value auctions with incomplete information. In short, the winner's curse says that in such an auction, the winner will tend to overpay. However, an actual overpayment will generally occur only if a bidder fails to account for the winner's curse when bidding. So despite its dire-sounding name, the winner's curse does not necessarily have ill effects. A Pyrrhic victory is a victory with devastating cost to the victor. ... A common value auction is a term in economics describing an auction in which the good being auctioned is valued the same by each participant. ... This article or section does not adequately cite its references or sources. ... Complete information is a term used in economics and game theory to describe a economic situation or game in which knowledge about other market participants or players is available to all participants and is instantaneously updated as new information arises. ...

Contents

Explanation

In a common value auction, the auctioned item is of roughly equal value to all bidders, but the bidders don't know the item's market value when they bid. Each player independently estimates the value of the item before bidding.


The winner of an auction is, of course, the bidder who submits the highest bid. Since the auctioned item is worth roughly the same to all bidders, they are distinguished only by their respective estimates. The winner, then, is the bidder making the highest estimate. If we assume that the average bid is accurate, then the highest bidder overestimates the item's value. Thus, the auction's winner is likely to overpay. In mathematics, an average or central tendency of a set (list) of data refers to a measure of the middle of the data set. ...


More formally, this result is obtained using conditional probability. We are interested in a bidder's expected value from the auction (the expected value of the item, less the expected price) conditioned on the assumption that the bidder wins the auction. It turns out that for a bidder's true estimate the expected value is negative, meaning that on average the winning bidder is overpaying. This article defines some terms which characterize probability distributions of two or more variables. ... In probability theory the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects as the outcome of the random trial when identical odds are...


Savvy bidders will avoid the winner's curse by bid shading, or placing a bid that is below their ex ante estimation of the value of the item for sale - but equal to their ex post belief about the value of the item, given that they win the auction. The key point is that winning the auction is bad news about the value of the item for the winner. It means that he/she was the most optimistic and if bidders are correct in their estimations on average, that too much was paid. Therefore savvy bidders revise their ex ante estimations downwards to take account of this effect. In an auction, bid shading describes the practice of a bidder placing a bid that is below what they believe a good is worth. ... Ex ante is a Latin term meaning beforehand. Ex ante evaluations deal with forecasting and forecasted returns on invested money. ... Ex ante is a Latin term meaning beforehand. Ex ante evaluations deal with forecasting and forecasted returns on invested money. ...


The severity of the winner's curse increases with the number of bidders. This is because the more bidders, the more likely it is that some of them have overestimated the auctioned item's value. In technical terms, the winner's expected estimate is the value of the first order statistic, which increases as the number of bidders increases. In statistics, the kth order statistic of a statistical sample is equal its kth-smallest value. ...


There is often confusion that winner's curse applies to the winners of all auctions. However, it is worth repeating here that for auctions with private value (i.e. when the item is desired independent of its value in the market), winner's curse does not arise.%%


Examples

Since most auctions involve at least some amount of common value, and some degree of uncertainty about that common value, the winner's curse is an important phenomenon.


In the 1950s, when the term winner's curse was first coined, there was no accurate method to estimate the potential value of an offshore oil field. So if, for example, an oil field had an actual intrinsic value of $10 million, oil companies might guess its value to be anywhere from $5 million to $20 million. The company who wrongly estimated at $20 million and placed a bid at that level would win the auction, and later find that it was not worth as much. Drilling rig in a small oil field Near Sarnia, Ontario, 2001 An oil field is an area with an abundance of oil wells extracting petroleum (oil) from below ground. ...


Other auctions where the winner's curse is significant:

A Spectrum auction is a process whereby governments use an auction system to sell the rights to broadcast over specific electromagnetic wavelengths. ... Legend: γ = Gamma rays HX = Hard X-rays SX = Soft X-Rays EUV = Extreme ultraviolet NUV = Near ultraviolet Visible light NIR = Near infrared MIR = Moderate infrared FIR = Far infrared Radio waves: EHF = Extremely high frequency (Microwaves) SHF = Super high frequency (Microwaves) UHF = Ultra high frequency VHF = Very high frequency HF = High... Nickname: Big Apple, Gotham, NYC, City That Never Sleeps, The Concrete Jungle, The City So Nice They Named It Twice Location in the state of New York Coordinates: Country United States State New York Boroughs The Bronx Brooklyn Manhattan Queens Staten Island Settled 1676  - Mayor Michael Bloomberg (R) Area    - City... An initial public offering (IPO) is the first sale of a corporations common shares to public investors. ... Market capitalization, often abbreviated to market cap, mkt. ... It has been suggested that shareholder be merged into this article or section. ...

See also

In game theory the War of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while accumulating costs at a constant rate c. ... A heroic failure is a loss or losing draw, in which the losing side has actually gained the moral upper hand. ... In general use, a no-win situation is one where a person has choices, but no choice leads to success. ... This page is a candidate to be moved to Wiktionary. ... In the film Reservoir Dogs, Eddie, Joe, and Mr. ... A Pyrrhic victory is a victory with devastating cost to the victor. ...

External links


Google, Inc. ... In North American professional sports, particularly baseball, football, and basketball, a free agent is a team player whose contract with a team has expired, and the player is able to sign a contract with another team. ...

 view  Topics in game theory

Definitions Game theory is often described as a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ...

Normal form game · Extensive form game · Cooperative game · Information set · Preference In game theory, normal form is a way of describing a game. ... It has been suggested that Game tree be merged into this article or section. ... A cooperative game is a game where groups of players (coalitions) may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players. ... In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed so far. ... Preference (or taste) is a concept, used in the social sciences, particularly economics. ...

Equilibrium concepts Price of market balance In economics, economic equilibrium is simply a state of the world where economic forces are balanced and in the abscence of external shocks the (equilibrium) values of economic variables will not change. ... In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...

Nash equilibrium · Subgame perfection · Bayes-Nash · Trembling hand · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · ESS · Risk dominance In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ... Subgame perfect equilibrium is an economics term used in game theory to describe an equilibrium such that players strategies constitute a Nash equilibrium in every subgame of the original game. ... In game theory, a Bayesian game is one in which information about characteristics of the other players (i. ... The trembling hand perfection is a notion that eliminates actions of players that are unsafe because they were chosen through a slip of the hand. ... In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. ... Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson. ... Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme. ... In game theory, an evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a strategy which if adopted by a population cannot be invaded by any competing alternative strategy. ... Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten. ...

Strategies In game theory, a players strategy, in a game or a business situation, is a complete plan of action for whatever situation might arise; this fully determines the players behaviour. ...

Dominant strategies · Mixed strategy · Tit for tat · Grim trigger In game theory, dominance occurs when one strategy is better or worse than another regardless of the strategies of a players opponents. ... In game theory a mixed strategy is a strategy which chooses randomly between possible moves. ... Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ... Grim Trigger is a trigger strategy in game theory for a repeated game, such as an iterated prisoners dilemma. ...

Classes of games

Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. ... Perfect information is a term used in economics and game theory to describe a state of complete knowledge about the actions of other players that is instantaneously updated as new information arises. ... In game theory, a sequential game is a game where one player chooses his action before the others chooses theirs. ... In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ... Signaling games are dynamic games with two players, the sender (S) and the receiver (R). ... Cheap Talk is a term used in Game Theory for pre-play communication which carries no cost. ... Zero-sum describes a situation in which a participants gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). ... Mechanism design is a sub-field of game theory. ...

Games Game theory studies strategic interaction between individuals in situations called games. ...

Prisoner's dilemma · Coordination game · Chicken · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game · Public goods game · Nash bargaining game Will the two prisoners cooperate to minimize total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In game theory, the prisoners dilemma is a type of non-zero-sum game in which two players can cooperate with... In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ... It has been suggested that Peace war game be merged into this article or section. ... The Battle of the Sexes is a two player game used in game theory. ... In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. ... Matching Pennies is the name for a simple example game used in game theory. ... The Ultimatum game is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. ... Minority Game is a game proposed by Yi-Cheng Zhang and Damien Challet from the University of Fribourg. ... Rock, Paper, Scissors chart Listen to this article · (info) This audio file was created from an article revision dated 2006-07-13, and may not reflect subsequent edits to the article. ... The Pirate Game is a simple mathematical game. ... The dictator game is a very simple game in experimental economics, similar to the ultimatum game. ... The Public goods game is a standard of experimental economics; in the basic game subjects secretly choose how many of their private tokens to put into the public pot. ... The Nash Bargaining Game is a simple two player game used to model bargaining interactions. ...

Theorems

Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's Theorem Minimax is a method in decision theory for minimizing the expected maximum loss. ... In game theory, the purification theorem was contributed by Nobel laurate John Harsanyi in 1973[1]. The theorem aims to justify a puzzling aspect of mixed strategy Nash equilibria: that each player is wholly indifferent amongst each of the actions he puts non-zero weight on, yet he mixes them... In game theory, folk theorems are a class of theorems which imply that in repeated games, any outcome is a feasible solution concept, if under that outcome the players minimax conditions are satisfied. ... The revelation principle of economics can be stated as, To any equilibrium of a game of incomplete information, there corresponds an associated revelation mechanism that has an equilibrium where the players truthfully report their types. ... In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox demonstrates the impossibility of designing a set of rules for social decision making that would meet all of a certain set of criteria. ...

Related topics

Mathematics · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... This article or section does not cite its references or sources. ... Nobel Prize in Economics winner Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ... Evolutionary game theory (EGT) is the application of game theory in evolutionary biology. ... Population genetics is the study of the distribution of and change in allele frequencies under the influence of the four evolutionary forces: natural selection, genetic drift, mutation, and migration. ... Behavioral ecology is the study of the ecological and evolutionary basis for animal behavior, and the roles of behavior in enabling an animal to adapt to its environment (both intrinsic and extrinsic). ... Adaptive Dynamics is a set of techniques for studying long-term phenotypical evolution developed during the 1990s. ... This is a list of notable economists, mathematicians, political scientists, and computer scientists whose work has added substantially to the field of game theory. ...


 
 

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