Abstract
A counterexample is given to Lemma 1 of Ray and Vohra (2019). This lemma is a key part of the proof of the main theorem (Theorem 1) of the cited paper. We give an additional condition under which Lemma 1 holds. This 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.
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