Discussion paper

DP16048 A Network Solution to Robust Implementation: the Case of Identical but Unknown Distributions

We consider mechanism design environments in which agents commonly know that others’ types are
identically distributed, but without assuming that the actual distribution is common knowledge, nor
that it is known to the designer (common knowledge of identicality). We study partial and full implementation, as well as robustness. First, we characterize the transfers which are incentive compatible under common knowledge of identicality, and provide necessary and
sufficient conditions for partial implementation. Second, we characterize the conditions under which
full implementation is possible via direct mechanisms, as well as the transfer schemes which achieve full
implementation whenever it is possible. We do this by pursuing a network approach, which is based on
the observation that the full implementation problem in our setting can be conveniently transformed
into one of designing a network of strategic externalities, subject to suitable constraints which are
dictated by the incentive compatibility requirements entailed by common knowledge of identicality. This approach
enables us to uncover a fairly surprising result: the possibility of full implementation is characterized
by the strength of the preference interdependence of the two agents with the least amount of preference
interdependence, regardless of the total number of agents and their preferences. Finally, we study robustness properties of the implementing transfers with respect to misspecification of agents’ preferences and lower orders beliefs in rationality.

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Citation

Ollár, M and A Penta (eds) (2021), “DP16048 A Network Solution to Robust Implementation: the Case of Identical but Unknown Distributions”, CEPR Press Discussion Paper No. 16048. https://cepr.org/publications/dp16048