The theory of regular economies is useful for the studies of the local uniqueness of equilibria, continuity of the equilibrium price correspondence, and possibility of comparative statics. The theory of regular economies also helps give a better understanding of the core correspondence, because...

1. The Economic Framework -- 2. Introduction to the Mathematics -- 3. Differentiable Manifolds and Mappings, Tangents, Vectorfields -- 4. Regular Equilibria. A First Approach -- 5. Scarf’s Example -- 6. Excess Demand Functions -- 7. Debreu’s Theorem on the Finiteness of the Number of...

We consider an oligopolistic market with a given finite number of price setting firms. We study the dependence of the market share of a firm on its own price and give conditions on the distribution of consumers' characteristics such that the profit of a firm becomes a quasiconcave function of...