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Model This!

Doug with medical kit

It’s not unusual to receive emails from former students, but the subject line “Strange Request” caught my eye. The email, received early on a Saturday morning, was from a recent graduate of the UT Physician EMBA program and it went something like this:

Well, here is an unusual circumstance. I am flying out to LA today to be on a pilot TV show called "Final Offer." The whole show is designed around negotiation between knowledgeable collectors and fine antique dealers. I am bringing a duplicate neurosurgical set to sell to one of 4 dealers and they have a set of rules (e.g., once you leave a room you cannot go back to the same dealer). Sounds like the kind of puzzle you would discuss in class! The filming is on Monday and I'd like to speak to you by phone if you have some time this weekend...

The former student, Doug Arbittier, is an anesthesiologist from York, Pennsylvania who is a serious collector of antique medical equipment; and I mean serious to the point that his enormous collection is housed in a beautiful museum that he built on his family’s property (view it here).

We connected by phone the day before the taping and he filled in a few important details about the show. First, he knew who the four dealers were and had an approximate idea about their level of knowledge and, perhaps, interest in the item he was bringing. Second, each dealer would be in a separate room and Doug would get to choose the sequence of negotiations. Third, and very importantly, the dealers would not know their order in the sequence. Hence, a dealer would not know if he were first or last in the sequence of negotiations. Doug specifically needed help not only in determining a sequence, but also a strategy for negotiation, i.e., what to reveal and whether to accept an offer or not.

Immediately my mind searched for a modeling framework. Was it a sequential decision making problem, multi-stage stochastic optimization with recourse, an auctioning problem, or some other classic management science problem? It seemed to have elements of all of these. As in any modeling effort, Doug and I discussed the relative certainties (what he could likely sell it for from his website, which was about $3500), the uncertainties (the “distributions” characterizing dealer knowledge and behavior), and his own objective function. An objective of simply maximizing selling price would fail to incorporate the value of “time on the air” to promote his medical antiques website and museum. For example, if he sold it to the first dealer for $3600, his appearance would be over and his gain would be not much more than the status quo. If, on the other hand, he was offered $10,000 by the first dealer then the monetary gain would likely compensate for the limited exposure. We both agreed that the amount of money at stake was certainly not life changing for him, thus giving the nod towards maximizing exposure time while still willing to sell at the right price.

His final strategy consisted of sequencing the dealers from least knowledgeable (and highly variable) to most knowledgeable (with likely efficient valuation). Also, we discussed a sequence of minimum “acceptance thresholds” of $5000, $4500, $4000, and $3500, corresponding to the four dealers. This strategy would help balance the tradeoff between airtime and selling price. In other words, he would be willing to settle for a lower price by the time he got to the third or fourth dealer.

The bottom line is that you never know when you’ll be asked to model a situation and it’s rare that it will fit nicely into a known framework. By asking lots of questions and listening carefully, you can help bring out the key elements and then apply concepts and principles of familiar models.

So, how did it work out for Doug? Read on...

...Well, it turned out that approximating dealer knowledge and interest beforehand was harder than he thought. The first dealer was still recovering from a recent surgery and the mere thought of anything surgical conjured up such bad memories that he had absolutely no interest in the set. The second dealer was more interested than originally estimated and, after some intense negotiations, made a final offer for the set for $4000. Although this was quite close to Doug’s threshold value of $4500 (and led to a dramatic pause as he left the room), he decided to decline the offer and take his chances with the two remaining dealers. Surprisingly, the third dealer offered a measly $500 and the fourth dealer gave a final offer of $2500. Inhindsight, from a dealer’s perspective, $2500-3000 may be an appropriate value for an item that can sell on the open market for $3500 since they must be rewarded for their risk with a reasonable profit. From Doug’s perspective, however, he got an all-expense paid trip to Los Angeles, 15-minutes of TV fame, and a chance to share his passion to a much larger audience - not a bad deal afterall.

Dr. Charles Noon