I Leilão de Artes Organismo, 04/03/06
Salvador Dalí
Homme d’une complexion malsaine, écontant le bruit de la mar
1929, Âleo s/ Madeira, 23,5 x 34,5 cm
Lance Inicial: 1.000 (hum mil) dracmas
Winner’s curse
From Wikipedia, the free encyclopedia
The Winner’s curse is a phenomenon akin to a Pyrrhic victory that occurs in common value auctions with incomplete information. In such an auction, the goods being sold have a similar value for all bidders, but players are uncertain of this value when they bid. Each player independently estimates the value of the good before bidding.
The winner of an auction is, of course, the bidder who submits the highest bid. When each bidder is estimating the good’s value and bidding accordingly, that will probably be the bidder whose estimate was largest. If we assume that on average the bidders are estimating accurately, then the person whose bid is highest has almost certainly overestimated the good’s value. Thus, a bidder who wins after bidding what they thought the good was worth has almost certainly overpaid.
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 good, less the expected price) conditioned on the assumption that the bidder won the auction. It turns out that for a bidder bidding their true estimate, this expected value is negative, meaning that on average the winning bidder is overpaying.
Savvy bidders will avoid the winner’s curse by bid shading, or placing a bid that is below what they believe the good is worth. This may make it less likely that the bidder will win the auction, but it also protects them from overpaying in the cases where they do win. A savvy bidder knows that they don’t want to win if it means they will pay more than a good is worth. To minimize bid shading, many auctions such as eBay have the bidder pay the price of the highest losing bid. (Note, however, that this lessens but does not necessarily eliminate the winner’s curse, because the highest losing bid may still be above the good’s value.)
The severity of the winner’s curse gets stronger as the number of bidders increases. This is because the more bidders there are, the more likely it is that some of them have greatly overestimated the good’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.
Claude Monet
Marine França
1880-1890, Âleo s/ Tela, 65 x 91 cm
Lance Inicial Organismo: 1 (um) talento de prata
A Terceira Margem do Rio, João Guimarães Rosa
Nosso pai era homem cumpridor, ordeiro, positivo; e sido assim desde mocinho e menino, pelo que testemunharam as diversas sensatas pessoas, quando indaguei a informação. Do que eu mesmo me alembro, ele não figurava mais estúrdio nem mais triste do que os outros, conhecidos nossos. Só quieto. Nossa mãe era quem regia, e que ralhava no diário com a gente ââ?¬â? minha irmã, meu irmão e eu. Mas se deu que, certo dia, nosso pai mandou fazer para si uma canoa.
Era a sério. Encomendou a canoa especial, de pau de vinhático, pequena, mal com a tabuinha da popa, como para caber justo o remador. Mas teve de ser toda fabricada, escolhida forte e arqueada em rijo, própria para dever durar na água por uns vinte ou trinta anos. Nossa mãe jurou muito contra a idéia. Seria que, ele, que nessas artes não vadiava, se ia propor agora para pescarias e caçadas? Nosso pai nada não dizia. Nossa casa, no tempo, ainda era mais próxima do rio, obra de nem quarto de légua: o rio por aí se estendendo grande, fundo, calado que sempre. Largo, de não se poder ver a forma da outra beira. E esquecer não posso, do dia em que a canoa ficou pronta.
Sem alegria nem cuidado, nosso pai encalcou o chapéu e decidiu um adeus para a gente. Nem falou outras palavras, não pegou matula e trouxa, não fez a alguma recomendação. Nossa mãe, a gente achou que ela ia esbravejar, mas persistiu somente alva de pálida, mascou o beiço e bramou: ââ?¬â? “Cê vai, ocê fique, você nunca volte!” Nosso pai suspendeu a resposta. Espiou manso para mim, me acenando de vir também, por uns passos. Temi a ira de nossa mãe, mas obedeci, de vez de jeito. O rumo daquilo me animava, chega que um propósito perguntei: ââ?¬â? “Pai, o senhor me leva junto, nessa sua canoa?” Ele só retornou o olhar em mim, e me botou a bênção, com gesto me mandando para trás. Fiz que vim, mas ainda virei, na grota do mato, para saber. Nosso pai entrou na canoa e desamarrou, pelo remar. E a canoa saiu se indo ââ?¬â? a sombra dela por igual, feito um jacaré, comprida longa.
Nosso pai não voltou. Ele não tinha ido a nenhuma parte. Só executava a invenção de se permanecer naqueles espaços do rio, de meio a meio, sempre dentro da canoa, para dela não saltar, nunca mais. A estranheza dessa verdade deu para. estarrecer de todo a gente. Aquilo que não havia, acontecia.
(continue a ler aqui “A terceira margem do rio”, de João Guimarães Rosa)
Henri Matisse
Le Jardin de Luxembourg França
1903
Âleo s/ Tela
Lance Inicial Organismo: 5.000 (cinco mil) sestércios
Determinacy from elementary considerations
Familiar real-world games of perfect information, such as chess or tic-tac-toe, are always finished in a finite number of moves. (It is an instructive exercise to figure out how to represent such games as games in the context of this article.)
If such a game is modified to assign a draw to a particular player (for example, if we say that Black wins draws at chess), such games are always determined. The condition that the game is always over in a finite number of moves (“over” in the sense that all possible extensions of the finite position result in a win for the same player) corresponds to the topological condition that the set A giving the winning condition for GA is clopen in the topology of Baire space.
The proof that such games are determined is rather simple: Player I simply plays not to lose; that is, he plays to make sure that player II does not have a winning strategy after I’s move. If player I cannot do this, then it means player II had a winning strategy from the beginning. On the other hand, if player I can play in this way, then he must win, because the game will be over after some finite number of moves, and he can’t have lost at that point.
This proof does not actually require that the game always be over in a finite number of moves, only that it be over in a finite number of moves whenever II wins. That condition, topologically, is that the set A is closed. This fact–that all closed games are determined–is called the Gale-Stewart theorem. Note that by symmetry, all open games are determined as well. (A game is open if I can win only by winning in a finite number of moves.)
Pablo Picasso
La Dance
1956, Âleo s/ Tela, 100 x 81 cm
Lance Inicial: 50.000 (cinqüenta mil) pedras de mó da Melanésia, com furo ou sem furo (sortida).
Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory. It was formulated in 1904 by Ernst Zermelo. While it was originally controversial, it is now used without embarrassment by most mathematicians. However, there are still schools of mathematical thought, primarily within set theory, that either reject the axiom of choice, or even investigate consequences of axioms inconsistent with AC.
Intuitively speaking, AC says that given a collection of bins, each containing at least one object, then exactly one object from each bin can be picked and gathered in another bin – even if there are infinitely many bins, and there is no “rule” for which object to pick from each.
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Druga obala.
Misli lako prelaze
ostatke mosta.
The other bank.
thoughts easily cross
the remains of the bridge.
L’ autre rive.
Les pensées facilement
franchissent les ruines du pont.
Das andere Ufer.
Gedanke überschreiten leicht
die Reste der Brücke.
vamos tagear, tagear tagear…
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