BeckerDeGrootMarschak

The Becker-DeGroot-Marschak mechanism (BDM) is a method in experimental economics for eliciting an individual’s true willingness to pay for a good or service. Proposed by Gary Becker, Morris DeGroot, and Jacob Marschak in 1964, it combines a bid with a random price draw to create incentives that encourage truthful reporting of value under certain conditions.

Mechanism: The participant states a bid b as the maximum they are willing to pay. A price p is drawn from a known probability distribution F independently of the bid. If p ≤ b, the participant buys the good at price p; if p > b, no purchase occurs. The allocation and payment are determined ex post by the comparison of b and p.

Properties: The mechanism is incentive-compatible in dominant strategies for independent private values when the price distribution is common knowledge. The best action is to bid the true value v, yielding expected payoff E[(v − p) 1{p ≤ v}] if bidding truthfully. It is robust under many standard experimental conditions, but its optimality relies on risk neutrality and accurate knowledge of F. Risk aversion, misperceptions about the price distribution, or strategic misreporting can distort bids.

Applications: Used to estimate valuations and demand curves in laboratory and field experiments; useful when actual purchase of the item may be impractical; allows researchers to recover willingness-to-pay distributions without bargaining.

Variants: Different price distributions, continuous or discrete, and adjustments for multiple units or budget constraints.

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