Contest vs. Competition in Cournot Duopoly: Schaffer's Paradox

Abstract: The paper compares two types of industrial organization in the Cournot duopoly: (a) the classical one, where the market players maximize profits and the outcome of the game is a Cournot-Nash equilibrium; (b) a contest in which players strive to win a fixed prize/bonus employing unbeatable strategies. Passing from (a) to (b) leads to a perfect competition with zero profits of the players (Schaffer's paradox). Transition from (b) to (a) results in a substantial decline in the production output, which also seems paradoxical, as it is commonly accepted that competition increases efficiency. We examine these phenomena in two versions of the Cournot model: with a homogeneous good and with differentiated goods.