Stability and competitive equilibria in multi-unit trading networks with discrete concave utility functions
The authors introduce the multi-unit trading network model and study its stability properties and competitive equilibria. In this model, valuation functions of each agent are twisted \(M^{\natural}\)-concave functions defined on the set of integer vectors. The generalized full substitutes condition is introduced and the authors show that this condition is equivalent to twisted \(M^{\natural}\)-concavity. Furthermore, they show that there exists a competitive equilibrium under the generalized full substitutes condition and that the set of competitive equilibrium price vectors forms a lattice. The relationship between competitive equilibria, stability, and efficiency is considered. It is proved that a competitive equilibrium is stable, and a competitive equilibrium trade vector is efficient. The relation between the three stability concepts stability, strong group stability and chain stability is discussed and it is shown that these concepts are equivalent under the generalized full substitutes condition.
twisted \(M^{\natural}\)-concave functions
scientific article; zbMATH DE number 6482430
scientific article