We study a noncooperative game of coalition formation, based on an underlying game in coalitional form. We introduce order independent equilibria (OIE). A strategy profile is an OIE if, for any specification of first movers in the sequential game, it remains an equilibrium and leads to the same payoff. Our results are: (1) Payoffs in OIE that use pure, stationary strategies must be in the core of the underlying game in coalitional form. (2) If the underlying game has the property that all its subgames have nonempty cores then, for each payoff vector, there exists an OIE with the same payoff. Journal of Economic Literature Classification Numbers: C70, C71, C72, C78. © 1995 Academic Press. All rights reserved.