The starting point for your assignment should be discussing the focus of Groupon's business. While the initial model of "pushing" emails of local coupon deals into mailboxes was successful for a short period, the company's stock prices collapsed shortly after its IPO and it has been trying to re-invent itself, moving to a "pull" model for its core business, moving more heavily into general discount online retailing, and moving into the food delivery market. From a business perspective, it might actually be better for Groupon to solidify its core business strategy before trying to expand randomly in every direction. Its main strength is its early start in mobile marketing; its main weakness, a lack of direction and uneven results with its core group coupon business.
The key to expanding as a platform company is that platforms tend to be natural monopolies. Attracting large numbers of vendors attracts large numbers of customers and then the the large customer base attracts more vendors, starting a virtuous cycle. This means expanding piecemeal into a large range of new markets is not an appropriate business strategy. Instead, it makes sense to target a few carefully selected markets where it might be possible to achieve dominance. This would be done best by forming partnerships or strategic alliances, as the route to success is eliminating competition. As detailed understanding of local buying habits is needed, much of the marketing and other decisions should be done locally.