NoteDrugs, guns, and targeted competition

•Three drug cartels compete for the control over their regional markets.•Cartels can vary the degree of their competition on a per-rival basis.•The game is differential. The solution concept is a Markov Perfect Equilibrium.•If cartels are myopic, then the strongest cartel eventually wins.•If cartels are sufficiently forward-looking, they converge.

We consider a dynamic competition game involving three players, in which 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, then 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.