Farsighted coalitional stability is the idea that when a coalition decides whether or not to deviate from a status quo, it considers further coalitional deviations that may occur subsequently. Ray and Vohra (2019) study optimality conditions on deviations in such settings. Unfortunately, a key lemma in their paper does not hold. In Maximality in the farsighted stable set revisited, I give an additional condition under which the lemma holds.
My condition specifies that when a coalition of players T is broken up by the participation of some of its players in an coalitional move by S , then the new coalitions and payoffs for the remainder of the players T \ S depend on neither the coalitions and payoffs of players outside of T before the breakup, nor the coalitions and payoffs of players outside of T \ S after the breakup, nor the identities of players in S who are not members of T.
Published as Corrigendum to maximality in the farsighted stable set in Econometrica (2020). Link to paper.
Thumbnail image is the assassination of Julius Caesar, depicted in a woodcut image by Johannes Zainer circa 1474.