Immunity to credible deviations from the truth

We study a notion of non-manipulability by groups, based on the idea that only some agreements among potential manipulators may be credible. The derived notion of immunity to credible manipulations by groups is intermediate between individual and group strategy-proofness. Our main non-recursive definition turns out to be equivalent, in our context, to the requirement that truthful preference revelation should be a strong coalition-proof equilibrium, as recursively defined by Peleg and Sudhölter (1998, 1999). We provide characterizations of strategy-proof rules separating those that satisfy it from those that do not for a large family of public good decision problems.