With the technical development of the reading equipment, e-books have witnessed a gradual and steady increase in sales in recent years. Last year, smart phones announced to be able to perform additional functions as e-book reading devices, making it possible for retailers selling e-books for smart phones (SPR) such as iPhone to differentiate with those selling e-books for specific reading equipment (SER) such as Amazon Kindle. We develop a game theory model to examine the competition between SER and SPR retailers. We derive the equilibrium price and analyze the factors that affect equilibrium outcomes under both scenarios of complete and incomplete information. Our results suggest that reduced cost due to inconvenience of reading e-books over iPhone lowers equilibrium prices, and reduced cost of specific reading equipment leads to more intense price competition. Under information asymmetry, we show that SER retailers will increase the price at equilibrium.