Affine equations as dynamic variables to obtain economic equilibria

Abstract

This thesis studies how economic equilibria can be reached with limited information by adjusting affine equations, and how collusion in oligopolistic markets can be maintained with affine reaction strategies. The first question is considered for exchange economies, contracting problems, and a two-party negotiation support method. The main contributions are new ways to reach and maintain equilibria.

For exchange economies the thesis shows that a modification of fixed-point iteration converges globally under conditions that are remarkably close to those required for the continuous time tâtonnement process presented by Arrow, Block, and Hurwicz. For the constraint proposal method for two-party negotiations this thesis provides answers for three major questions: does the method produce Pareto-optimal points, does it lead to a problem that has a solution, and can the solutions be found with fixed-point iteration. The thesis also shows that the complete information equilibrium of a contract design problem can be reached by adjusting the contract with fixed-point iteration. Finally, the thesis formulates a simple dynamic counterpart of a static reaction strategy by D. K. Osborne in a repeated oligopoly game with discounting. It is proven that these strategies lead to a subgame perfect equilibrium when the possible deviations are bounded and the proportional reaction strategies have sufficiently large slopes.