Perfect Price Equilibrium and Social Influence on Choices

We study a usual duopoly game with a two‐stage game. In the first stage firms choose their prices and in the second stage individuals choose in which firm they are going to buy. The inicialsetup isthe Bertrand price model. We add a new term to the utilities of the individuals: the social influence in choices. We are able to fully characterise the local perfect equilibria: some individuals decide to be loyal to some firm and others choose a mix strategy. Our new model brings a new understanding of the Bertrand paradox.