FYI : According to Facebook Promotions Guidelines all contests need to be administered through 3rd party apps.
Sometimes, all you need to increase the level of interaction on your Facebook Page is to sweeten the deal a bit with a little contest. This will not only give people a reason to keep on checking your page, but it will also increase the exposure of your brand and excite new brand fans of to join your page. Here are some contest ideas that you can refer to for inspiration.
The “Tag” Marketing
Simply post a picture of your product or your brand on a weekly or monthly bases and ask your fans to tag themselves in various parts of the picture for a chance to win either the items tagged or some other prize. IKEA was probably one of the first brands to leverage this technique effectively and it was a great hit with their fans.
While a scavenger hunt might be a bit more taxing on the contestants, its benefit is that it forces contestants to check your information a bit more in-depth. You can create a scavenger hunt on Facebook by laying out a trail of clues that might stretch over from your social media presence into your website or even Google maps. Buick is about to run another contest in their series of city focused scavenger hunts, which have been very successful in the past.