The Discretization of Continuum Strategy Spaces

Carlos Alós-Ferrer, University of Konstanz

Abstract

When the strategy set of a game is a continuum, its discretization may not conserve local properties even for arbitrarily fine strategy grids. Two technical lemmas are proven to solve the problem, one relying on differentiability properties and another for higher dimensions formulated for open-graph correspondences. Four applications are shown, regarding the discretization of Cournot and Bertrand settings, a consumer optimization problem, and an insurance market.