On the tacit collusion equilibria of a dynamic duopoly investment game

This note extends the characterization of simultaneous investment (tacit collusion) equilibria in Boyer, Lasserre and Moreaux (2012). Tacit collusion equilibria may or may not exist, and when they do may involve either finite time investments (type 1) or infinite delay (type 2). The relationship between equilibria and common demand forms is not immediately apparent. We provide the full necessary and sufficient conditions for existence. A simple condition on demand primitives is derived that determines the type of equilibria. Common demand forms are then shown to illustrate both finite-time and infinite-delay tacit collusion.