Smooth, Ex-post Implementation with Multi-dimensional Information. ———————————————————————– Preliminary and Incomplete, Do Not Cite ———————————————————–
نویسنده
چکیده
A social-choice function maps reports of the agents’ private information into a set of social alternatives. The (weak) expost implementation problem is to find transfers such that truthful reporting by the agents is ex-post incentive compatible. Jehiel et al. (2006) prove that in enviroments with a discrete set of social alternatives, at least two agents, multi-dimensional information and generic preferences, only constant social-choice functions are ex-post implementable. In this paper, we study mechanisms where the outcome space of the social-choice function is continuous (e.g., random allocations) rather than discrete as in JMMZ. In addition, we restrict attention to smooth social-choice functions, where the differential approach can be used. First, we provide a simple proof that extends their impossibility result to our environment when the dimension of the outcome space (i.e., the number of instruments) is one (e.g., random allocations between two alternatives) and the dimensional of an agent signal space is 2 or larger. The proof shows that the only smooth social choice functions that satisfy the local, first-order incentive compatibility constraints for ex-post implementation are constant functions. In the case when the outcome space has dimension equal or larger than 2N and there are N agents with bidimensional signals, we show that it is possible to satisfy the local, first order incentive compatibility constraints.
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