Rock, paper… Christie’s

When it comes to changing diapers, Erika and I try to alternate when we are both home. Occasionally, however, we lose track of whose turn it is, in which case we resort to the time-honored tradition of rock, paper, scissors. That was flashing through my head when I read this Caroline Vogel article in the New York Times (thanks to J.H. for the link):

It may have been the most expensive game of rock, paper, scissors ever played. Takashi Hashiyama, president of Maspro Denkoh Corporation, an electronics company based outside of Nagoya, Japan, could not decide whether Christie’s or Sotheby’s should sell the company’s art collection, which is worth more than $20 million, at next week’s auctions in New York. He did not split the collection – which includes an important C?zanne landscape, an early Picasso street scene and a rare van Gogh view from the artist’s Paris apartment – between the two houses, as sometimes happens. Nor did he decide to abandon the auction process and sell the paintings through a private dealer. Instead, he resorted to an ancient method of decision-making that has been time-tested on playgrounds around the world: rock breaks scissors, scissors cuts paper, paper smothers rock…. After each house had entered its decision, a Maspro manager looked at the choices. Christie’s was the winner: scissors beat paper.

After re-reading the article, however, what I found particularly interesting about this story is the contrast between these two paragraphs. There’s this one:

In Japan, resorting to such games of chance is not unusual. “I sometimes use such methods when I cannot make a decision,” Mr. Hashiyama said in a telephone interview. “As both companies were equally good and I just could not choose one, I asked them to please decide between themselves and suggested to use such methods as rock, paper, scissors.”

This actually makes sense — when the decision-making costs exceed the payoff differential between the two choices, this is a rational decision. However, this leads to an interesting question — is rock, paper, scissors a game of chance? While Hashiyama faced a minimal difference in payoffs between his choices, both Sotheby’s and Christie’s saw a whopping difference between getting nothing or getting some sizeable commissions from Hashiyama’s business. Given this gap in payoffs between winning and losing, Christie’s thought it was worth doing some strategic research:

Kanae Ishibashi, the president of Christie’s in Japan, declined to discuss her preparations for the meeting. But her colleagues in New York said she spent the weekend researching the psychology of the game online and talking to friends, including Nicholas Maclean, the international director of Christie’s Impressionist and modern art department. Mr. Maclean’s 11-year-old twins, Flora and Alice, turned out to be the experts Ms. Ishibashi was looking for. They play the game at school, Alice said, “practically every day.” “Everybody knows you always start with scissors,” she added. “Rock is way too obvious, and scissors beats paper.” Flora piped in. “Since they were beginners, scissors was definitely the safest,” she said, adding that if the other side were also to choose scissors and another round was required, the correct play would be to stick to scissors – because, as Alice explained, “Everybody expects you to choose rock.”

Sotheby’s thought of the game as a strict game of chance, and did no research. Given that there are apparently rock paper scissors championships and rock-paper-scissors strategy guides (and please, someone tell me if these are hoax sites), who was right — Christie’s or Sotheby’s? [Christie’s won, so isn’t the answer obvious?–ed. In a one-shot game, it’s not clear that Christie’s won because of research; they might have won because of chance. A normal-form version of this game reveals that the only equilibrium strategy is to randomize equally among the three options. However, this might be a game where the designations of “rock, paper, scissors” alters how human beings feel about the choices, which subtly alters their expectations of what other players will do, which then alters their own strategies. In other words, a formal model of rock, paper, scissors might not carry the crucial piece of information to optimize on strategy. Now you’re making my head hurt–ed. Aha! This is evidence to support the original claim; even if there might be a strategic element to this game, that element is so small that it’s outweighed by the computational costs of figuring out the optimal strategy against a specified opponent!!] “Good ol’ rock. Nothing beats that. D’Oh!!” Bart Simpson.