Drugs, Guns, and Targeted Competition

Abstract

We consider a dynamic competition game among three players, where each player can vary the extent of his competition on a per-rival basis. We call such competition targeted. We show that if the players are myopic, the weaker players eventually lose the game to their strongest rival. If instead the players are sufficiently far-sighted, then all three players converge in their power and stay in the game. We develop our model in application to drug wars, but the approach of targeted competition can be applied to competition between firms or political parties, or to warfare.

Keywords: targeted competition, dynamic oligopoly, differential games, drug wars

JEL Classification: C73, D43