The Mechanism

A buyer asks a supplier what it would cost to make a component. The supplier knows; the buyer can observe the finished part, but cannot see the cost behind it. A promise to reimburse whatever the supplier reports gives expensive answers a conspicuous advantage. The difficulty survives the most carefully worded question, because the answer changes the payment. Mechanism design begins here, with the rules that make a report consequential. Game theory usually takes those rules as given and asks what the players will do. Read backward, it asks what rules would lead them to produce a desired result. The designer specifies the messages people may send, the allocation that follows, and the payments attached to it. Private knowledge enters the calculation through the choices the rules induce. A truthful answer becomes usable when the person who knows has reason to give it.¹

Incentive compatibility puts that reason into a comparison the designer must satisfy for every possible type. A supplier should earn at least as much by reporting its actual cost as by making any other permitted report. Participation adds a separate comparison: taking the offered deal must be at least as attractive as the supplier’s outside option. In a game with many informed parties, the equilibrium concept also matters. A dominant-strategy rule makes truth optimal whatever the others report; a Bayesian incentive-compatible rule makes it optimal in expectation when the others follow their prescribed strategies and the relevant beliefs are used. Both are precise requirements. Neither requires truth to be the uniquely best response in every case. An indifferent participant can have several optimal messages, so an equilibrium in which everyone reports truthfully is a more exact claim than a promise that the rules compel honesty.²

The honest supplier can consequently retain a surplus that perfect observation would let the buyer remove. Suppose the component is worth 25 to the buyer and costs either 10 or 20 to make, each with probability one half. There is one supplier, both parties value money linearly, and declining the transaction yields zero. Production is worthwhile at either cost. If the buyer could verify cost, it could pay 10 to one type and 20 to the other, leaving itself an expected gain of 10. With hidden cost, that same payment rule invites the cheap supplier to report 20. Buying from both types while satisfying their reporting constraints requires the same payment for either report; voluntary production by the expensive type requires at least 20. At that payment, the cheap supplier keeps 10 and the expensive supplier keeps zero. The expected information rent is 5, and the buyer’s expected gain falls to 5. The component is still made whenever making it creates a gain. Information has changed the division of that gain.³

A buyer seeking a larger private return can reduce the rent by reducing the expensive type’s chance of trade. Offer production with certainty and payment 15 after a report of low cost, and production with probability one half and expected payment 10 after a report of high cost. The cheap supplier earns 5 under either report. The expensive supplier earns zero by reporting truthfully and would lose 5 by claiming to be cheap. With truthful reporting and participation when indifferent, expected production is three quarters, expected payment is 12.5, and the buyer’s gain is 6.25. Expected total gains fall from 10 to 8.75, because half the worthwhile high-cost production is lost. The buyer can go further: a payment of 10 for low-cost production and no high-cost trade yields an expected gain of 7.5, while eliminating the supplier’s rent. These comparisons expose the choice behind the contract. Saving on information rents can reward the buyer while destroying some gains from trade. If the two costs were identical and known, the reporting conflict would disappear.

The revelation principle makes this search manageable by replacing an elaborate game with the reports that reproduce its equilibrium. Imagine that the supplier normally bargains through several rounds, choosing a strategy according to its private cost. A direct mechanism can instead ask for the cost, simulate the strategy that this type would have used, and deliver the resulting allocation and payment. A profitable false report would then correspond to a profitable deviation in the original game: the supplier could have adopted the other type’s strategy there. If the original strategies formed an equilibrium, that deviation was already unattractive. Truthful reporting therefore reproduces the selected equilibrium outcome. The principle gives the designer a disciplined way to search across achievable arrangements, carrying their incentive constraints into a common form. It creates no additional resources and grants no access to a fact that the original arrangement could not elicit.⁴

The direct representation preserves the economic conditions that made the represented outcome possible. The buyer must be able to commit to the announced payments; the delivered component must satisfy the observable specification; the supplier must face the outside option used in the calculation. A buyer who invites a report and then rewrites the price has offered a different game. Likewise, an additional profitable equilibrium or a coalition of participants can require analysis beyond the individual reporting constraints just imposed. The revelation principle establishes the existence of a truthful equilibrium corresponding to the chosen one; it supplies no general guarantee that every equilibrium selects the designer’s preferred outcome. Applying the theory thus requires attention to the actual messages, verification, enforcement and beliefs. Myerson’s auction analysis itself closes with the dependence of the design on the model’s information and valuation assumptions.⁵

The purpose built into the rules determines which of these feasible bargains is called best. A buyer minimizing its payment, a supplier protecting its return, and an institution seeking the largest total gains can favor different arrangements even when they agree about every probability and cost. The mathematics exposes their trade-offs and the constraints on pursuing them. It leaves the authority to choose the objective with whoever writes the rules. Honesty can be made a best policy, and the honest can still collect a rent; that is part of the price of eliciting knowledge from someone free to withhold or misdescribe it. The next plate considers a cheaper, more troubling substitute for learning the person’s private type. The Stereotype turns to the group taken as a proxy for the individual, and to the opportunities that can disappear inside an average.