Core and competitive equilibria with indivisibilities

Abstract

Abstract:The paper presents a model of an exchange economy with indivisible goods and money.There are a finite number of agents, each one initially endowed with a certain amount of money and at most one indivisible good. Each agent is assumed to have no use for more than one indivisible good. It is proved that the core of the economy is nonempty. If utility functions are increasing in money, and if the initial resources in money are in some sense "sufficient" the core allocations coincide with the competitive equ~brium allocations.With restrictions on the set of feasible allocations, the same model is used to prove the existence of stable solutions in the generalized "marriage problem". However it is shown that, even ff money enters the model, these solutions cannot generally be obtained as competitive equilibria.

A model of partnership formation

“…Our analysis is closely related to the models on assignment markets studied by Koopmans and Beckmann (1957), Shapley and Shubik (1972), Shapley and Scarf (1974), Crawford and Knoer (1981), Kelso and Crawford (1982), Svensson (1983), Quinzii (1984), Kaneko and Yamamoto (1986), and Yamamoto (1987). In their classic papers, Koopmans and Beckmann (1957) and Shapley and Shubik (1972) investigate assignment markets from the viewpoint of equilibrium theory and cooperative game theory, respectively.…”

Competitive Equilibrium in an Exchange Economy with Indivisibilities

“…Preferences are strictly supermodular if the inequality in (22) is strict whenever S 3 T 3 S (or equivalently if the inequality in (23) is strict whenever T 2 {, and T 3 {,). From (22) it is clear that supermodularity implies superadditivity. If N contains at most two objects then superadditivity implies supermodularity.…”

“…Submodular preferences are subadditive. Preferences are additive if the inequality in (22) is replaced by an equality, or equivalently, if…”

“…The difference is that in assignment markets each agent desires only one indivisible objects whereas in our model agents have interdependent values over several indivisible objects. Another related group of papers are Quinzii [22], Gale [11], and Kaneko and Yamamoto [15]. These authors consider an exchange economy which is less general than the one considered in this paper in that each buyer has utility for one object only and more general in that they allow utility functions with income effects.…”

A simultaneous descending bid auction for multiple items and unitary demand

“…Crawford and Knoer (1981) introduced one of these mechanisms, which is a generalization of the deferred acceptance algorithm of Gale and Shapley (1962). Quinze (1984), Kaneko (1982), Kaneko and Yoshitsugu (1986), Alkan (1988), Alkan (1992) and Alkan and Gale (1988) prove the existence of competitive equilibria in a more general model.…”