Pricing in population games with semi-rational agents

We consider a pricing game in which two competing sellers offer two similar products on a social network among agents (communities). Each agent chooses, in an iterative manner, between the two products depending on what his neighbours do. This introduces two separate games; one between the agents and one between the two sellers. We show that the first game is a full potential game and provide a polynomial time algorithm to compute where the game converges to. We also study various properties of the second games such as its equilibrium points and its convergence.