How to Deal with One Important Barrier to Effective Mediation

Victoria Pynchon, at the Settle It Now Blog, reviews some well known cognitive biases to effective problem solving for mediators and negotiators. 

But, one of the things that does surprise me is how little relevant game theoretic illusions have made their way into the mainstream literature. These illusions do have special applications to mediation.

Consider, one of my favourites, the dollar auction game, invented by Professor M. Shubik.

Here is the set-up, one of the easier set-ups to analyze. Mr. Auctioneer proposes to auction off a $20.00 bill to Mr. Clever and Ms. Swift. The winning bid gets the $20.00, but the loser has to throw in the value of his or her bid.

For example, if Mr. Clever bids $5, and Ms. Swift's losing bid was $4, then Mr. Clever gets the $20.00 for $5, and Mr. Auctioneer also gets $4 from Ms. Swift.

Each player has to bid at least once.

So how does the betting go, as between Mr. Clever and Ms. Swift?

Well, Ms. Swift jumps out first with a bid of $2, to which Mr. Clever increases to $2.50. Ms. Swift, right on the mark, goes to $5.00, and Clever counters with $5.25. Swift jumps to $10.00; Clever counters with $10.10. Swift takes a pause and jumps to $19.00; Clever takes a longer pause and then cleverly bids $20.00 and grins at Swift.

Swift is now not living up to her name, because after much reflection she realizes that if she passes now, she is out $19.00, whereas if she bids $20.50, and is the winning bid, then she will only be out 50 cents - and so the bid of $20.50 for a $20.00 bill.

Mr. Clever realizes, quickly, the strategic situation also and ventures a cautious $21.00 - better to lose $1 than $20.00.

Our heroes eventually end up paying Mr. Auctioneer somewhere between $50 and $60 for a $20.00 bill, sadly vowing never to play this stupid game again, until next time that they are in this situation and don't recognize it, in an expensive lawsuit perhaps?

This real illusion has been played out many times in experimental games and the conclusion appears to be: don't play this game. You cannot buy a $20.00 bill for less than $50.00?

Well let's debug this illusion with a bit of game theoretic logic.

First, if the Swift and Clever could act as one person, then Swift could bid 1 cent, Clever bid 2 cents, and Swift could pass, letting Clever obtain $20.00 for a net profit of $19.98.

This is their maximum joint gain- what they could obtain if they could give up control of their actions to some coordination device, something like a stop sign or line-up in real life.

Knowing their joint gain, how can Clever persuade Swift not to bid again, after the 2 cent bid?

Well, what if he pulled out a $10 spot, waved in front of Swift's nose, got her to smell the real coin of the realm, and handed it over to her after her no bid? Or put the $10. on the table and asked Swift for 2 cents? Put 2 cents on the table and asked Swift for a "loan" of $10.00, offering as collateral his 2 cents and promise not to bid if Swift went to 3 cent?

All of these commitment devices will allow Clever and Swift to share their joint gain.

Now, there is no guarantee that once the individuals see what their joint gain could be that they will find the necessary commitment devices that will drive them to their joint goal.

Indeed, game theory's preoccupation with Nash solutions has obscured this fact.

But repeat after me:

"We will find joint gains as the result of coordination, then we will look for commitment devices to split the joint gain, because our strategies are probably off the Nash equilibrium path."

Does that do anything for you?