zbMATH — the first resource for mathematics

Job matching, coalition formation, and gross substitutes. (English) Zbl 0503.90019
Summary: Competitive adjustment processes in labor markets with perfect information but heterogeneous firms and workers are studied. Generalizing results of L. S. Shapley and M. Shubik [Int. J. Game Theory 1, No. 2, 111–130 (1972; Zbl 0236.90078)], and of V. P. Crawford and E. M. Knoer [Econometrica 49, 437–450 (1981)], we show that equilibrium in such markets exists and is stable, in spite of workers’ discrete choices among jobs, provided that all workers are gross substitutes from each firm’s standpoint. We also generalize D. Gale’s and L. S. Shapley’s [Am. Math. Mon. 69, 9–15 (1962; Zbl 0109.24403)] result that the equilibrium to which the adjustment process converges is biased in favor of agents on the side of the market that makes offers, beyond the class of economies to which it was extended by Crawford and Knoer [loc. cit.]. Finally, we use our techniques to establish the existence of equilibrium in a wider class of markets, and some sensible comparative statics results about the effects of adding agents to the market are obtained.

91B40 Labor market, contracts (MSC2010)
91B68 Matching models
91B50 General equilibrium theory
Full Text: DOI