Core-stable rings in auctions with independent private values

► We start with a Bayesian game with independent private values, e.g., an auction. ► We associate a cooperative partition form game with the Bayesian game. ► We define core-stable coalitions in the partition form game. ► We illustrate that, in standard auctions, coalitions are core-stable. ► We show that coalitions may not be core-stable in auctions with externalities.