Pricing game of online display advertisement publishers

We consider online display advertisement publishers who maximize the revenue by optimal pricing in an oligopoly setting. Each publisher interacts with others through setting cost-per-impression (CPM) that affects the demand for everyone. Using the pseudoconcavity of the objective function, we prove that a unique best response Nash equilibrium exists for each publisher. We also consider the sensitivity of the publisher while other publishers changes their CPM. In both cases, the best response of the publisher depends entirely on her current best response CPM. We provide an algorithm for finding the equilibrium and illustrate by numerical examples.