The weak sequential core for two-period economies

We adapt the classical core concept to deal with situations involving time and uncertainty. We define the weak sequential core as the set of allocations that are stable against coalitional deviations ex ante, and moreover cannot be improved upon by any coalition after the resolution of uncertainty. We restrict ourselves to credible deviations, where a coalitional deviation cannot be counterblocked by some subcoalition. We study the relationship of the resulting core concept with other sequential core concepts, give sufficient conditions under which the weak sequential core is non-empty, but show that it is possible to give reasonable examples where it is empty.