This paper investigates marriage market equilibrium under the assumption that Bargaining In Marriage (BIM) determines allocation within marriage. Prospective spouses, when they meet in the marriage market, are assumed to foresee the outcome of BIM and rank prospective spouses on the basis of the utilities they foresee emerging from BIM. Under these assumptions, the marriage market is the first stage of a multi-stage game -- in the simplest case, a two-stage game -- that must be solved by backwards induction. The marriage market determines both who marries and, among those who marry, who marries whom. Bargaining in the second and any subsequent stages determines allocation within each marriage. When BIM determines allocation within marriage, the appropriate framework for analyzing marriage market equilibrium is the Gale-Shapley matching model.
In contrast, the standard model of marriage market equilibrium assumes that prospective spouses make Binding Agreements in the Marriage Market (BAMM) that determine allocation within marriage. If we assume BAMM and transferable utility, then the appropriate framework for analyzing marriage market equilibrium is the Koopmans-Beckmann-Shapley-Shubik assignment model. BIM and BAMM have different implications not only for allocation within marriage but also for who marries, who marries whom, the number of marriages, and the Pareto efficiency of marriage market equilibrium.