If you mean a traditional "fighting game", where 2 players control 2 fighters, and jump, punch, kick and use special moves, this will be a difficult project. As you may have noticed, even AAA commercial studios with multi-million dollar budgets still have a hard time getting sufficient bandwidth throughput and low enough latency to carry out the highly-twitch based gameplay of a fighter. They get closest due to highly experienced network programmers who have a figurative toolbox overflowing with tricks and hacks.
However, all is not lost, that is for sure. Some simple tweaks to your gameplay could mean the difference between horrendous lag and a fast-paced, workable end product.
I would suggest checking out Halls
Impact and Node.js tutorial series. Impact is a great HTML5 game engine that would allow you to make real-time browser games that could be ported to Android and iOS fairly simply. While it is more focused on an MMORPG style of game, I would still suggest it, and then work at branching that out into more fast-paced games, such as fighting games, with some experience
