Robust implementation under alternative information structures

Abstract

In this paper we consider a model in which agents have complete infonnation about their neighbors and, possibly, incomplete infonnation about the rest of the environment. We consider two different informational frameworks. In the first, agents do not have priors about the relevant characteristics in the rest of the environment. In the second, agents are supposed to have priors about the unknown characteristics. We present a mechanism which implements any social choice correspondence satisfying monotonicity and no veto power in both informational settings for every possible prior thus requiring little knowledge from the point of view of the designer of the information possessed by agents about the environment.

Equivalence of Nash implementability and robust implementability with incomplete information

“…As a corollary of Proposition 1 and Theorem 1, we have Corchon and Ortufio-Ortin's [2] sufficiency conditions for robust implementation with respect to a restricted class of information structures under some additional assumptions on the set of alternatives and preferences. [2]) Suppose that (1) …”

“…With this issue in mind, we discuss the following stronger concept of implementation recently proposed by Corchon and Ortufio-Ortin [2]. An SCS is said to be robustly implementable if there exists a mechanism such that for each possible information structure, the set of equilibrium outcomes for that structure coincides with the SCS.…”

“…Corchon and Ortufio-Ortin [2] consider the design of such a robust mechanism in a society consisting of several groups such that (i) there are at least three agents in each group; and (ii) each agent knows the preferences of the agents in his group but has incomplete information about the preferences of the agents outside his group. Examples of such groups include departments in an organization, firms in an industry, and countries in an international market.…”

“…In this case, the equilibrium concept is uniform Nash equilibrium. (2) Risk. Every agent has a prior distribution over the set of possible types of the agents outside his group.…”

“…When information is complete and a certain condition of closure is satisfied, the two definitions are equivalent (see Postlewaite and Schmeidler [18], Palfrey and Srivastava [15,17], and Jackson [8]). 2 We allow for an incomplete information group in which some agents have prior distributions on types, but the others do not.…”