We consider a dynamic (differential) game with three players competing against each other. Each period each player can allocate his resources so as to direct his competition towards particular rivals -- we call such competition selective. The setting can be applied to a wide variety of cases: competition between firms, competition between political parties, warfare. We show that if the players are myopic, the weaker players eventually loose the game to their strongest rival. Vice versa, if the players value their future payoffs high enough, each player concentrates more on fighting his strongest opponent. Consequently, the weaker players grow stronger, the strongest player grows weaker and eventually all the players converge and remain in the game.

differential games, dynamic oligopolies, selective competition
Stochastic and Dynamic Games; Evolutionary Games (jel C73), Oligopoly and Other Forms of Market Imperfection (jel D43)
Tinbergen Institute
Tinbergen Institute Discussion Paper Series
Discussion paper / Tinbergen Institute
Tinbergen Institute

Dubovik, A, & Parakhonyak, A. (2009). Selective Competition (No. TI 2009-072/1). Discussion paper / Tinbergen Institute. Tinbergen Institute. Retrieved from http://hdl.handle.net/1765/16519