Econometrica: Jan 2007, Volume 75, Issue 1

Overcoming Incentive Constraints by Linking Decisions

https://doi.org/10.1111/j.1468-0262.2007.00737.x
p. 241-257

Matthew O Jackson, Hugo F Sonnenschein

Consider a Bayesian collective decision problem in which the preferences of agents are private information. We provide a general demonstration that the utility costs associated with incentive constraints become negligible when the decision problem is linked with a large number of independent copies of itself. This is established by defining a mechanism in which agents must budget their representations of preferences so that the frequency of preferences across problems mirrors the underlying distribution of preferences, and then arguing that agents' incentives are to satisfy their budget by being as truthful as possible. We also show that all equilibria of the linking mechanisms converge to the target utility levels. The mechanisms do not require transferable utility or interpersonal comparisons of utility, and are immune to manipulations by coalitions.

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Comments & Corrigenda

Comment on Jackson and Sonnenschein (2007) “Overcoming Incentive Constraints by Linking Decisions”

WE CORRECT A BOUND in the definition of approximate truthfulness used in the body of the paper of Jackson and Sonnenschein (2007). The proof of their main theorem uses a different permutation-based definition, implicitly claiming that the permutation-version implies the bound-based version. We show that this claim holds only if the bound is loosened. The new bound is still strong enough to guarantee that the fraction of lies vanishes as the number of problems grows, so the theorem is correct as stated once the bound is loosened.

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