Incentive compatibility

In typical strategic interactions under incomplete information, different types (of a player) can choose from among a menu of different actions (strategies) that comprises the possibility that they mimic the behavior of other types (of the same, or of another player). Incentive compatibility conditions ensure that different types (of each player) align themselves such that they can be identified by their equilibrium choices. Typically, they are used to prevent that some type profits from copying another type's action (given the other types do not disguise themselves behind others' choices). More generally, incentive compatibility conditions force a desired constellation of choices to form a strategic equilibrium for a given array of types. In particular, they might as well ensure that it be worthwhile for different types to choose the same action (the types pool on an action). Yet in most economic problems, incentive compatibility conditions serve to induce a strategic equilibrium which reveals the players' private information by having them choose different 'characteristic' equilibrium actions, i.e. they have the types 'sort themselves out'.

For a simple example, suppose several buyers that differ in their private (marginal) valuations of some economic good (their types) select the quantity to buy from a seller. If the seller maximizes his proceeds from sale, he will want the buyers with higher valuations to buy higher quantities, i.e. she will want to separate her customers (or market segments) according to their marginal willingness-to-pay. To have such choices form a strategic equilibrium, the seller has to provide incentives to the high- valuations customers to buy higher quantities and to prevent market segments with lower valuations from profitably micking the choices of high-valuation customers. To meet both ends, it is often enough to simply offer a monotonic reward scheme that links choices to rewards. In the example, it is enough that the seller rewards buying higher quantities by offering a schedule of ever larger price discounts for larger quantities bought.

The basic idea that is with a monotonic reward scheme, lower types cannot find it worthwhile to mimic the choices of higher types because higher types themselves find it worthwhile to choose even more extreme actions which, in the end, are too costly to copy for lower types. Thus, the price of having the types self-select by giving monotonic rewards to them necessitates that higher types are rewarded progressively higher rents for revealing their information, relative to lower types. (For an illustration of this point, see the paragraph on information rents in the entry rents.)

More generally, suppose the types are 'naturally ordered' in terms of increasing marginal profitability (or costliness) of some economic action; e.g., the schedule of marginal willingnesses-to-pay is differently steep for different customers; different candidates have differently steep marginal cost schedules in investing varying amounts in some activity, etc. Then, to put it in jargon, any monotonic reward scheme "provides incentives to the types to separate themselves", i.e. it has the players self-select levels of actions which reveal the natural ordering of their types.

Incentive compatibility conditions occur throughout economics with incomplete information because, as we have tried to argue, they are closely related to strategic equilibria with certain features. Most often, incentive compatibility constraints are used to frame the ways of interaction such as to create equilibria where the players' private information is revealed by their equilibrium choices. Among important applications are the theory of optimal taxation of unobservable behavioral characteristics in public finance, optimal selling schemes in non-linear pricing and auctions, the optimal regulation of firms under incomplete information, or incentive wage contracts eliciting effort inputs from employees that can hide shirking under favorable conditions.

Entry by: Jan Vleugels

December 1, 1997
Direct questions and comments to: Glossary master