2017/06/01 by Babaioff, Moshe, Blumrosen, Liad, Nisan, Noam
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1706.00219
We consider a price competition between two sellers of perfect-complement goods. Each seller posts a price for the good it sells, but the demand is determined according to the sum of prices. This is a classic model by Cournot (1838), who showed that in this setting a monopoly that sells both goods is better for the society than two competing sellers. We show that non-trivial pure Nash equilibria always exist in this game. We also quantify Cournot's observation with respect to both the optimal welfare and the monopoly revenue. We then prove a series of mostly negative results regarding the convergence of best response dynamics to equilibria in such games.