On the ubiquity of duopolies in constant sum congestion games

We analyse a coalition formation game between strategic service providers of a congestible service. The key novelty of our formulation is that it is a constant sum game, i.e., the total payoff across all service providers (or coalitions of providers) is fixed, and dictated by the size of the market. The game thus captures the tension between resource pooling (to benefit from the resulting statistical economies of scale) and competition between coalitions over market share. In a departure from the prior literature on resource pooling for congestible services, we show that the grand coalition is in general not stable, once we allow for competition over market share. In fact, under classical notions of stability (defined via blocking by any coalition), we show that no partition is stable. This motivates us to introduce more restricted (and relevant) notions of blocking; interestingly, we find that the stable configurations under these novel notions of stability are duopolies, where the dominant coalition exploits its economies of scale to corner a disproportionate market share. Furthermore, we completely characterise the stable duopolies in heavy and light traffic regimes.