Corporate reputation is more and more the most valuable asset for a firm. In this day and age, corporate reputation, although an intangible asset, is and will grow as the most essential asset to publicize and also protect. Social media are a formidable tool to publicize a firm's brand and improve its reputation. However, it can also be deadly. Associated with social media comes the "buzz"", i.e. the means to spread at an unprecedented speed and scale any information, being true or false. In this paper, our aim is to propose a Game Theory approach with both a finite and an infinite horizon. The model presented here helps us evaluate the impact of social media on a firm's reputation. It also highlights the important parameters of a firm's reputation in this new digital era"