Information elicitation and sequential mechanisms
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- Aricha, I. & Smorodinsky, R. Int J Game Theory (2013) 42: 931. doi:10.1007/s00182-012-0346-6
We study an incomplete information mechanism design problem with three peculiarities. First, access to agents’ private information is costly and unobservable. Second, the mechanism may communicate sequentially with the agents. Third, the mechanism designer and all the agents share a common interest. As an example one can think of N geologists that study the potential oil reserves in some tract. The geologists agree on the right course of action, given their N studies. However, carrying out the study may be costly for a geologist and so he may opt to fabricate a study. The oil company that employs these geologists need not contract them simultaneously and may, furthermore, choose to provide some of the results of early studies to geologists employed later on. Finally, the geologists and the oil company would like the joint study to forecast the quantity of oil reserves as accurate as possible. It turns out that, in such settings, what may not be implementable without communication becomes implementable with communication. Clearly, the possibility for sequential communication introduces a lot of complexity to the design problem. However, we provide a result in the spirit of the revelation principle and argue that whenever implementation is possible with communication it is also possible with a simple communication mechanism. Formally, we extend the model and results in Smorodinsky and Tennenholtz (Games Econ Behav 55(2):385–406, 2006) who consider the similar problem but restrict attention to symmetric social choice functions and IID distributions over the private information.