Expectation Formation Rules and the Core of Partition Function Games

This paper proposes axiomatic foundations of expectation formation rules, by which deviating players anticipate the reaction of external players in a partition function game. The axioms single out the projection rule among the rules that depend on the current partition and the pessimistic rule among the ones that are independent of the current partition. This analysis suggests that the projection core and the pessimistic core are natural candidates to study the stability of games in partition function form, and we compute these cores in two standard applications of coalition formation with externalities, namely cartels and public goods