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 projection rule is the only rule satisfying subset consistency and responsiveness to the original partition of non-deviating players. It is also the only rule satisfying subset consistency, independence of the original partition of deviating players, and coherence of expectations. Exogenous rules are the only rules satisfying subset consistency and independence of the original partition, and the pessimistic rule is the only rule generating superadditive coalitional games.