Overcoming Incentive Constraints by Linking Decisions

Abstract

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.

Efficiency in Games With Markovian Private Information

“…To motivate the construction, it is instructive to start with iid costs. Jackson and Sonnenschein (2007) show that when costs are iid (i.e., p = 1 2 ), a mechanism that satisfies (1) and (2) can be obtained by assigning to each firm a budget of reports with T 2 reports of each type. This linking mechanism approximately satisfies (1) for T large enough by the law of large numbers.…”

“…The construction is inspired by the linking mechanism of Jackson and Sonnenschein (2007), who use message budgets to force the long-run distribution of each player's reports to match his true type distribution.…”

Fair linking mechanisms for resource allocation with correlated player types

“…Related literature could be found in economics on cooperation [7,21] or similar problems in P2P systems such as reputation [20] and artificial currencies [12]. The work closest to our own, and in which we have based our proposal, is the linking mechanism proposed by Jackson and Sonnenschein [17,18]. Related to this work, Engelmann and Grimm [8] presents experimental research on linking mechanisms.…”

“…At a first sight, this strategy may seem a very poor punishment, given that there is always a chance that the player emerges victorious in her lie. However, this is not only enough to discourage dishonest players, but also a crucial ingredient to guarantee that our mechanism has the right properties, as formally shown in [18,33] for similar scenarios, and in the simulations below (see Sect. 6).…”

“…Recently, some mechanisms without payments have been proposed, like those of Procaccia and Tennenholtz [28], or the seminal work of Jackson and Sonnenschein [17,18] in which a new type of mechanism (called linking mechanism) is proposed. A linking mechanism, instead of offering incentives or payments to players, limits the spectrum of players' responses to a probability distribution known by the game designer.…”