Stable Matching in a Marriage Market When Preferences are Heterogeneous

In this paper I define a static marriage game with a continuum of players, when the traits of men and women are distributed uniformly, and agents have heterogeneous preferences. I interpret the continuum as the approximation of a large finite set of agents, and therefore define the core as the set of feasible allocations with the property that no finite coalition can improve upon its outcome. I prove that the core is non-empty, and is unique to the extent that any given agent gets the same pay-off in every core allocation. Consider a sequence of economies, characterized by finite sets of men and women, each set refining its predecessor, and converging in the limit to the interval that characterizes the continuum economy. I prove that there exists a sequence of core allocations of the finite economies such that the pay-off to any given agent along the sequence converges to his/her unique pay-off in the continuum economy