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aggregate equilibrium value aggregate welfare allowed transitions assets assumption A2 asymptotically efficient break-up coalition 12 coalition formation coalitional bargaining game condition Condorcet winner context contradiction control structure convergence Corollary defined denote economies without negative economy v,p,6 efficient externality-free equal probability equation equilibrium payoffs ergodic classes ergodic set excess of player exchange economies finite number firm flows of payoffs Formally game theory game with partition Gomes grand coalition Hart and Moore implies inefficient inequalities intermediary Jehiel limit long run properties Markov chains Markov Perfect Equilibrium mergers Moldovanu move negative externalities number of steps pairwise coalition Pareto Efficiency partition function patient players payoffs and transition Proof of Proposition proposer proposer's probabilities Q.E.D. Proof Ray and Vohra requires the consent result Section setup Shapley value side-payments solution concepts stable set strategy profile subsection sufficiently patient Suppose transition relation transition rule v-economy vs(a vs(b xs(b