We study a dynamic coalition-formation process in the tradition of Konishi and Ray (2003): players repeatedly form and dissolve binding agreements, evaluate states by discounted long-term expected payoffs, and hold self-confirming beliefs about the process. States and payoff sharing follow Heitzig and Kornek (2018): a state is a hierarchy of nested agreements; agreements are formed by merging existing top-level coalitions, and are terminated together with all agreements containing them; and the members of a new agreement share the surplus it generates, measured against the state without that agreement. All payoff assumptions are structural. We prove that every grand state ever reached is absorbing, and that every absorbing state is grand, for every discount factor. A grand state is actually reached, almost surely, in three cases: small discount factors; three players; and, for any number of players and all discount factors, whenever every player prefers every grand state to every non-grand state in static payoffs, as when distributional stakes are smaller than each player's share of the efficiency gain. Otherwise the process can fail only by cycling for ever among non-grand states. We give exact necessary conditions on such a cycle, and show that for a fixed candidate cycle they reduce to a finite system of linear inequalities in the static payoffs, so the question is decidable. Solving it yields a counterexample: with four players and discount factor one half, under either termination rule, there is an equilibrium that cycles for ever, so the grand coalition need not form. The example survives a far-sighted variant of the sharing rule under which merging raises every player's discounted long-term payoff, not only the static one; there the merge is blocked purely by a better move available to a subgroup. Whether arrival can fail as the discount factor tends to one remains open.

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