Are Stable Demands Vectors in the Core of Two-Sided Markets? Some Graph-Theoretical Considerations

Abstract

Stable demand vectors for games in coalitional form satisfy three requirements: 1) Players’ demands are such that there are no leftovers in any coalition. 2) Each player’s demand is such that he can find at least one coalition, including himself, that can satisfy the demands of its members. 3) No player i is dependent on player j in the sense that i always needs j to form a coalition satisfying its members’ demands, while j does not need i in order to do so. Since the stability condition 3 focuses on pairs, we look at NTU games of pairs such as those arising from two-sided markets. For each demand vector we define a bipartite graph, and we use the Konig-Hall Theorem and its corollaries to study properties of those graphs. In particular, stable demands are shown to be in the core if the number of agents on each side of the market is not greater than four.