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Michael Webster's Resolution to the Shubik Dollar Auction Game

(photo:  Bill IV by cmiper)

We've had a lively discussion going about making agressive first offers, for which we are indebted to our regular readers Michael (da Game Man) Webster and mediators Chris Annunziata and Geoff (Coalface???) Sharp.  

Michael provided a link to his solution to the "Shubik" Dollar Auction Game that most of us have played in mediation seminars.  Because the game itself demonstrates just how irrational bargaining can be, and Michael's solution demonstrates how everyone can "win" when cooler heads prevail, I am quoting part of his post here and commending to my readers' attention the full post here.

Shubik reported [of the Dollar Auction Game described in Michael's post]:

"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 damn fool about it."

Without at all diminishing my respect for W.C. Fields, I venture to suggest that there is a more reasonable way to play this game as opposed to quiting. What is it? 

First, lets update the game to the 21st century and restrict it to two players. Replace the $1 with $20 and each bid must be a multiple of $1. Each person must bid at least once, or they can agree not to play at all. What should they do? Suppose first bidder bids $1, and second bidder pays $2, what is the first bidder's reasonable response? Right now, as a collective they are paying $3 to get $20, or netting $17. He should demand that the second bidder pay his $9.50 not to bid! Alternatively, second bidder can offer first bidder $9.50 not to bid again.

Then the second bidder will the $20, paying $2 to the auctioneer, $9.50 to first bidder and so he nets $8.50. First bidder gets $9.50, pays $1 to auctioneer and nets $8.50, jointly getting $17.00. As I see it, $8.50 is better than nothing, giving lie to the claim that you cannot get something for nothing.

This is why I usually defer to Michael's greater wisdom.  He can do the math.

Comments (9)

Read through and enter the discussion by using the form at the end
Michael Webster - October 25, 2007 1:09 PM

Thank-you for posting the link.

But, I don't think that the correct metaphor is "cooler heads". I may be wrong, and frequently am, but I see these problems as types of illusions: in the dollar auction game, there is the illusion that there can be no joint gain.

The bigger issue here is whether the experienced mediators, which I am not, find value in revisiting the standard mediation training devices or games using my methodology: look for joint gains, and then for commitment devices which ensure that everyone will do their part. Those commitment devices are unlikely to nash equilibrium or best response to a best response.

A nash equilibrium is the type of strategy a person who was playing solitaire would use: no other people, just us playing cards. (Without at all diminishing my respect for Nash and game theorists in general for their intellectual achievement, I think that real life conflict resolution is far edgier than the calm offered by the nash solution - where it doesn't matter what the other player does.

Vickie - October 25, 2007 8:54 PM

In my mediation experience, people have to cool down before they're able to recognize that looking for joint gains is a smart thing to do. They enter mediation angry and looking for an advantage because they don't want to be taken advantage of. They don't WANT to look for joint gains when they're in this state of mind. They're looking to WIN.

Michael Webster - October 26, 2007 10:16 AM

Vickie; That is very interesting. I wonder if there is some biological link between anger and the inability to see the solution to these type of puzzles? I think that there was something back awhile on your site referencing testorone levels and play in the ultimatum game.

Ben - October 26, 2007 11:23 PM

If the first bidder agreed not to bid again, then the second bidder would be up $20 (-2 to 18), so why shouldn't the first bidder demand $19.99 not to bid again? If the second player refused the first player could up his bid to $20, netting zero and forcing player 2 to take a $2 loss.

Vickie Pynchon - October 27, 2007 11:49 AM

It's not testosterone (as far as I know). It's about freeing the brain's higher cognitive centers from the primitive operations of the flight/fight mechanism centered in the amygdala.

My friend Ken Cloke likes to begin his mediation training sessions by saying, "look around the room. What do you see? . . . beat . . . PRIMATES."

We LOVE to think that we're rational but we're not.

The only chance we have to think as rationally as we are able is to free ourselves of as much fear and anger as we can without rendering ourselves defenseless against predators.

Then we can use our higher cognitive functions to do the kind of math that Ben and you suggest.

As in all things, it's all about balance.

Michael Webster - October 31, 2007 11:15 AM

Ben; You are correct, the solution I proposed is not a nash equilbrium. Just as reasonable people play the ultimatum game differently than economists, so should they play this game differently. If the first player demanded $19.99 to not bid and then bid $20.00, if refused. The second player can also be "pissed" and bid $21. My solution calls for the first bidder to credibly commit to not bidding, which I think he can do by pushing a $10 spot across the table.

Vickie; I think that you are probably right: we need to escape the flight/fight mechanism if we are going to mediate by solving a problem jointly. However, I think that there is more to it.

Consider Ben's approach to this game -an approach much admired by game theorists and economists. He quite correctly notes that my solution is not a best response to a best response -after all, the bidder could accept the offer not to bid, take the money and renege.

Ben sees the point of the game in different manner than I do. He can force his point of view upon me; he and I will then battle together and give money away to the auctioneer. It is as much about what we choose to see the point of the game as it is about rationality.

Sam - November 2, 2007 1:33 AM

Bid $19 at the start and the bidding will stop, netting $1.

Michael Webster - February 26, 2008 9:48 AM

Sam,two points.

1. The rules of game require each person to bid at least once.

2. Why would you settle for $1 if you could get close to $10?

Carson - January 24, 2013 4:48 PM

Today, I went to the beach front with my children.
I found a sea shell and gave it to my 4 year old daughter and said "You can hear the ocean if you put this to your ear." She placed the shell to her ear and screamed.
There was a hermit crab inside and it pinched her ear.
She never wants to go back! LoL I know this is entirely off topic but I had to tell someone!

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