Strategic complements and substitutes in bilateral oligopolies

This note analyzes the effect of product complementarity in a bilateral oligopoly. We show that offers of traders on the two sides of the market are strategic complements (substitutes) if and only if the two goods are substitutes (complements). The outcome of the bilateral oligopoly game converges monotonically to the competitive equilibrium, as the\nelasticity of substitution between the goods decreases to [minus infinite].