Robust coalitional implementation

The paper introduces coalition structures to study belief-free full implementation. When the mechanism designer does not know which coalitions are admissible, we provide necessary and almost sufficient conditions on when a social choice function is robustly coalitionally implementable, i.e., implementable regardless of the coalition pattern and the belief structure. Robust coalitional implementation is a strong requirement that imposes stringent conditions on implementable social choice functions. However, when the mechanism designer has additional information on which coalitions are admissible, we show that coalitional manipulations may help a mechanism designer to implement social choice functions that are not robustly implementable in the sense of Bergemann and Morris, 2009, Bergemann and Morris, 2011. As different social choice functions are implementable under different coalition patterns, the paper provides insights on when agents should be allowed to play cooperatively.