The theory behind the Auction

[Finarvyn]

Some love it, some hate it, but one aspect of the ADRP rules that make them distinct is the attribute auction.

Erick addresses this particular issue in this auction thread. I thought that it would be interesting to reprint both Erick's explanation and an excerpt from the original source so that any discussion would be easier.

I'm going to split each up into smaller posts for ease of reading...

[Finarvyn]

Erick says:

The whole system was designed late in the summer of 1986, after I had discussed the possibility of designing and writing an Amber Role-Playing Game with West End Games. It didn't take long, since I talked with the West End guys at Gencon (August 14th-17th, 1986), and the first play-test, with the first Attribute Auction, took place at the Michigan Gaming Center, before the end of August.

I was looking for a character creation system that would simulate the rivalry between Corwin and his siblings as presented by Roger Zelazny in the Chronicles of Amber. Neither of the two conventional choices, random generation or point allocation, seemed like it would work.

On the other hand, I loved the idea of a system where the players would start interacting, and even competing, even as they were involved in character creation.

Based on the books, it was pretty clear that there were four significant attributes. Clearly, Gerard was #1 in Strength, Benedict had the reputation for being first in Warfare, either Brand or Fiona was the leader in Psyche, and Corwin demonstrated outstanding Endurance throughout the series (growing back his eyeballs in record time, etc.).

The idea of a series of auctions seemed to fit, especially if it was clear that (1) the 'winner' of each would be, hand's down, the very best in that attribute, (2) that all points bid would be points spent, thereby creating a 'ladder' of ranking, and (3) that there could be secret buys afterward, creating the kind of uncertainty that we had seen in the rivalry between Corwin and Eric.

My biggest concern was that four Attribute Auctions would take too much time. Fortunately, they turned out to be a lot of fun, even in the very first play-test.

Fortunately there was a big turn-out, even more than I expected, so we had nineteen (19) participants, and some pretty spirited bidding. Psyche was especially crazy, with the top three bidding 92, 91 and 89 points.

Everyone thought that nineteen was way too large a group for a single role-playing game, and I agreed with enthusiasm.

"Don't worry," I said, "you'll be split into two entirely different groups, based on two entirely different versions of the Amber Universe. One group will play as children of the characters in the Roger Zelazny books. The other group will be in an entirely original universe, where the structure of Pattern and Chaos is similar, but not connected in the least with Dworkin's Amber."

Happily, the whole thing worked out wonderfully well. The characters were interesting and complex, and the players definitely carried some grudges from the auctions, in a way that made for really interesting rivalries. Those with access to some of the early Amberzines can see for themselves in Don Woodward's 'Carolan' character diary.

In recent years, I've suggested that people read about the game theory exercise called "The Dollar Auction," based on John von Neuman's work, and described beautifully in the Willam Poundstone book, "Prisoner's Dilemma."

Here's an on-line excerpt

NOTE: I reprinted this as well. Keep reading...

[Finarvyn]

Excerpts from "Prisoner's Dilemma" by William Poundstone

SHUBIK'S DOLLAR AUCTION

In their free time, Martin Shubik and colleagues at RAND and Princeton tried to devise new and unusual games. According to Shubik, the central question was, "Can we get certain pathological phenomena as well-defined games?" They wanted games you could actually play. "I don't believe any game that can't be played as a parlor game," Shubik told me.

In 1950, Shubik, John Nash, Lloyd Shapley, and Melvin Hausner invented a game called "so long sucker." This is a vicious game, played with poker chips, where players have to forge alliances with other players but usually have to betray them to win. When tried out at parties, people took the game seriously. ("We had married couples going home in separate cabs," Shubik recalls.)

Shubik posed the question of whether it was possible to incorporate addiction in a game. This question lead to the dollar auction. Shubik is uncertain who thought of the game first or whether it was a collaboration. In any case, Shubik published it in 1971 and is generally credited as the game's inventor.

In his 1971 paper, Shubik describes the dollar auction as an "extremely simple, highly amusing and instructive parlor game." A dollar bill is auctioned with these two rules:

1. (As in any auction) the dollar bill goes to the highest bidder, who pays whatever the high bid was. Each new bid has to be higher than the current high bid, and the game ends when there is no new bid within a specified time limit.

2. (Unlike at Sotheby's!) the second-highest bidder also has to pay the amount of his last bid – and gets nothing in return. You really don't want to be the second-highest bidder.

Shubik wrote, "A large crowd is desirable. Furthermore, experience has indicated that the best time is during a party when spirits are high and the propensity to calculate does not settle in until at least two bids have been made."

Shubik's two rules swiftly lead to madness. "Do I hear 10 cents?" asks the auctioneer – "5 cents?"

Well, it's a dollar bill, and anyone can have it for a penny. So someone says 1 cent. The auctioneer accepts the bid. Now anyone can have the dollar bill for 2 cents. That's still better than the rate Chase Manhattan gives you, so someone says 2 cents. It would be crazy not to.

The second bid puts the first bidder in the uncomfortable position of being the second-highest bidder. Should the bidding stop now, he would be charged 1 cent for nothing. So this person has particular reason to make a new bid – "3 cents." And so on

Maybe you're way ahead of me. You might think that the bill will finally go for the full price of $1.00 – a sad comment on greed, that no one got a bargain. If so, you'd be way too optimistic.

Eventually someone does bid $1.00. That leaves someone else with a second-highest bid of 99 cents or less. If the bidding stops at $1.00, the underbidder is in the hole for as much as 99 cents. So this person has incentive to bid $1.01 for the dollar bill. Provided he wins, he would be out only a penny (for paying $1.01 for a dollar bill). That's better than losing 99 cents.

That leads the $1.00 bidder to top that bid. Shubik wrote, "There is a pause and hesitation in the group as the bid goes through the one dollar barrier. From then on, there is a duel with bursts of speed until tension builds, bidding then slows and finally peters out." [/b]

[Finarvyn]

To finish SHUBIK'S DOLLAR AUCTION:

No matter what the stage of the bidding, the second-highest bidder can improve his position by almost a dollar by barely topping the current high bid. Yet the predicament of the second-highest bidder gets worse and worse! This peculiar game leads to a bad case of buyer's remorse. The highest bidder pays far more than a dollar for a dollar, and the second-highest bidder pays far more than a dollar for nothing.

Computer scientist Marvin Minsky learned of the game and popularized it at MIT. Shubik reported: "Experience with the game has shown that it is possible to 'sell' a dollar bill for considerably more than a dollar. A total of payments between three and five dollars is not uncommon." Possibly W. C. Fields said it best: "If at first you don't succeed, try, try again. Then quit. No use being a d**n fool about it."

Shubik's dollar auction demonstrates the difficulty of using von Neumann and Morgenstern's game theory in certain situations. The dollar auction game is conceptually simple and contains no surprise features or hidden information. It ought to be a "textbook case" of game theory.

It ought to be a profitable game, too. The game dangles a potential profit of up to a dollar in front of the bidders, and that profit is no illusion. Besides, no one is forced to make a bid. Surely a rational player can't lose. The players who bid up a dollar to many times its value must be acting "irrationally."

It is more difficult to decide where they go wrong. Maybe the problem is that there is no obvious place to draw the line between a rational bid and an irrational one. Shubik wrote of the dollar auction that "a game theory analysis alone will probably never be adequate to explain such a process."

So ... what do you think?

[trevelyan]

In the dollar auction the second place bidder alone (i.e. not third or lower placed bidders) pays in addition to the top bidder and yet has absolutely nothing to show for it. The first place bidder walks away with a dollar.

In an attribute auction, every bidder gets something of value, with each rank being superior to those below.

With three bidders for the dollar, the third place bidder will always be better off then the second place bidder, and likely the first place bidder (once the price tops $1). the same is not true for the attribute auction.

I'm inclined to think that the only viable strategy for the dollar auction is to jump in with a bid of $1 (and so guarantee not to make a loss) or else not to bid at all (which amounts to the same thing). The same is never true of an attribute auction.

[keltset]

An interesting concept. This is what gave Erick the idea to hold an attribute auction?