The Becker-DeGroot-Marschak (BDM) Method: Turning Theory into Spend

Last month I discussed the challenges of market research, and some ways to make researching our customers (particularly their willingness to pay) more accurate. TL;DR – just asking people what they think they would pay doesn’t work; instead, the more we can put our customers into realistic situations, especially spending their own money, the more accurate the research is going to be.

That’s why I love the Becker-DeGroot-Marschak (BDM) Method.

What exactly is BDM?

BDM is an incentive-compatible “sealed-bid + lottery”. Each participant states the maximum they are genuinely willing to pay (their reservation price). After that, the researcher draws a price at random from a pre-specified distribution.

What happens once the participant has decided on their reservation price?

• If the random price is equal to or below the participant’s stated figure, the participant must buy the product - but crucially they pay the random price, not the higher amount they offered.

• If the random price is above their stated figure, no transaction occurs – they walk away with nothing.

Because over-bidding risks over-paying and under-bidding risks missing out, the dominant strategy is to reveal one’s true maximum. Economists call that truth-telling or demand revelation.

For those of you who like lots of background reading, in theoretical terms BDM is essentially a one-shot, single-unit analogue of a Vickrey (second-price) auction, but with the “second price” replaced by a number drawn from a transparent probability distribution. I’ll leave it to you to read up on Vickrey auctions! If you are really curious and dig deep, you’ll discover that Google uses a variant of this type of auction for keywords bids in AdWords.

A step-by-step illustration

1. Define the item and the price range
   Suppose we want to test the price of a new craft-beer advent calendar. We decide the lottery will draw any whole pound between £10 and £60.

2. Inform and rehearse
   Walk respondents through a dummy round with something trivial (e.g. a chocolate bar) so they grasp the rules - comprehension is everything.

3. Collect individual bids
   Each person writes down, say, “£38”. The bids stay private.

4. Lock the bids
   If this is not done face-to-face, seal the bids before the draw - physical envelopes or a timestamped online form both work.

5. Draw the random price
   Spin a digital wheel or physical tombola and it lands on, for instance, “£32”.

6. Execute (or not) the transaction
   Anyone who bid £32 or more is obliged to buy the calendar at £32. Those who bid less walk away empty-handed.

7. Debrief and pay/ship immediately
   The credibility of BDM rests on the purchase feeling real, so preferentially the participants will actually buy the product at this point.

Why researchers and pricing teams love BDM

Individual-level WTP

Every respondent (whether they were above or below the random price) yields one hard data-point, so even modest samples can map an accurate demand curve.

Reduced hypothetical bias

Participants know they really might have to part with cash, so they think twice before low-balling (or high-balling).

Simple maths, rich output

Plot the cumulative distribution of bids and you instantly see optimum revenue points, break-even volumes, and the price-elasticity slope.

Flexible formats

Works in person, online with digital wallets, or even in classrooms using vouchers.

Strong empirical track record

Large-scale field trials - e.g. clean-water tablets in Ghana - show BDM bids predict actual take-up remarkably well. 

Peer-reviewed reliability

Management Science finds the mechanism “robust and replicable” across hundreds of experiments.

Common pitfalls - and how to avoid them

Poor understanding of the rules

Always include a dry run and a comprehension check.

Range effects and anchoring

Set a broad, credible lottery range - and be explicit that any price within that range is equally likely, or simply don’t tell them what the range is at all.

Lack of real consequence

If you are not going to ask the participants to actually buy the items, then use cash-back, vouchers, or similar so the ‘buy’ feels binding. If participants suspect it’s hypothetical, truth-telling collapses.

One product at a time

BDM is labour-intensive if you test dozens of variants. Narrow your stimuli first (e.g. via conjoint or best-worst) and let BDM fine-tune the final candidate’s price.

Regulatory or ethical hurdles

Where incentives are restricted (e.g. healthcare studies), consider gifting a proportionate honorarium rather than forcing a purchase.

Risk attitude distortions

BDM’s dominant-strategy proof assumes risk-neutral expected-utility maximisers. In other words, everyone in the study has the same attitude to risk. Risk-averse participants shade bids down; risk-seekers shade up. Build in a simple risk-preference task (e.g. Holt-Laury lotteries) and correct for systematic bias if necessary.

When to reach for BDM

• Early-stage concept testing - You’ve built a prototype and want a quick read on whether £25 or £45 is realistic.

• Premium extensions - For example, gauging the upper limit on a “founder’s edition” SaaS licence.

• Internal buy-in - Presenting Finance with a demand curve grounded in cash-backed behaviour often carries more weight than survey scores.

• Neuro-pricing studies - Pairing BDM bidding with fMRI lets neuroscientists observe how the ventromedial prefrontal cortex encodes subjective value when money is on the line.

Conversely, if you need to test bundles or competitor trade-offs, discrete-choice or CVM (Contingent Valuation Method) studies may scale better. BDM shines when depth of insight on a single offer outweighs breadth.

A BDM example

Let’s say you have invented a brand new product. It’s called The Widget, you wear it like a ring, and it’s a 100% foolproof voice-activated remote control for everything you own that can possibly be controlled. You can tell it to ‘unlock the car’ or ‘change the TV channel to BBC1’ or ‘disarm the home alarm system’. The battery lasts forever, and it’s no bigger or heavier than a wedding ring.

Next we bring together (for example) 100 people to get their opinions on the potential price. For the BDM to be meaningful, they need to all be in the target market for The Widget. There’s no point including a technophobe, for example, and asking them what price they would pay because it’s £0, they wouldn’t buy it under any circumstance; or including someone who couldn’t afford it.

First, we run a trial BDM selling them a banana. They all make a range of bids, we generate a random price, and everyone who bid the random price or higher gets to buy the banana at the random price.

Now that they understand how BDM works, we do the real thing. Importantly, we need to clearly demonstrate The Widget to them, explain how it differs from anything else on the market, explain what value they’ll get from it (e.g. it can’t be snatched from your hand, stolen from your pocket or accidentally drop, so it’s vastly more secure than anything else you use for these functions; etc). They have to thoroughly understand it.

We ask them to write down what they would pay. Then we generate the random number to get a test price.

Everyone who bid a higher price than the random one now gets to own The Widget; they pay the random price and go home happy.

We actually don’t care how many people bid above the randomly generated test price. We care about all the prices they were prepared to bid. We want to plot what that looks like. So start with the lowest price anyone was prepared to bid – at that price that person, and everyone else who was prepared to pay more, would buy The Widget. In other words, at that price 100 people would buy it.

Then go to the next lowest price – at that price 99 people would buy it. Keep doing this, plotting the number of buyers left at each price. Sometimes two or three would have bid the same price. Eventually you reach the person who bid the most – just one person would buy it at that price.

You’ve now got a price elasticity curve showing the % (i.e. out of 100) of people who would buy at any particular price.

You can therefore work out a revenue curve by multiplying each price times the number of people who were prepared to pay, and plotting that. Is there a maximum revenue? Better still, if you know what the fixed cost to make 100 Widgets is and the individual cost per Widget, you can work out the total cost for each level of demand. Subtract that from the revenue curve, and you can now see at what price you maximise profit.

Bringing it together

BDM turns the abstract notion of “willingness to pay” into a concrete, wallet-open decision. Used judiciously - and explained clearly - it can validate a value-based price long before you commit to a full launch.

Next time someone in the team says “let’s just ask customers what they think”, you can smile, pull out your tombola, and watch real buying decisions unfold.

Happy pricing!