Particle Core is another arduino like clone that supports wifi. The author combines it with Blynk, a simple tool to control the arduino via android, to open/close a garage door. I am not sure how secure this is against something like a replay attack. Figure this would cost about $30 in parts. Interesting bit about how the relays sometimes don’t work well when upside down.
http://makezine.com/projects/particle-core-garage-door-opener/