The Price of Anarchy in Parallel - Serial Competition with Elastic Demand

We study a game theoretic model of competing network service providers that are connected in parallel and serial combinations and that strategically price their service in the presence of elastic user demand. Demand is elastic in that it diminishes both with higher prices and latency, which in turn grows linearly with a network’s usage. To obtain our results, we make an analogy between the game and an electric circuit, in which the slope of each provider’s latency function is made to be analogous to electrical resistance. Our bound on efficiency loss depends on the ratio of the conductance of the circuit branch with highest conductance to the combined conductance of all the branches. In terms of the original problem, the bound measures how the worst-case efficiency loss increases as the capability of the system becomes more concentrated in a particular serial combination of players.