These people seem to have a variety of small systems for tracking animals. Their GPS systems are small and light, though I don't think they relay position back to a receiver w/o some other optional equipment.
http://www.lotek.com/avian.htm
No matter how I think of it I can't find a fool proof solution. Let's say you could package a GPS small and light enough to fit in/on an arrow and not drastically affect it's accuracy and range. In order to find the game it needs to transmit it's location. That means an uplink to a cell phone tower or some other radio link. Depending on where you hunt, it can be quite easy to be out of reach for the former. And that type of radio equipment is larger, heavier and more $$ than a simple RF link or beacon. Additionally GPS signal strength is easily degraded in heavy woods and that's with the antenna pointed up. What happens if the game lands on top of the arrow and GPS ?
So if a GPS isn't a good answer, then perhaps a simple RF beacon would be. The hunter then carries a Yagi type antenna to listen to where the "beeps" are the strongest. The good thing is that even if the game isn't found, the arrow plus electronics is cheap, some tens of $$s, so losing them isn't the $$$ penalty that losing a GPS arrow would be. The problem is that the RF will be line-of-sight and that means it may be blocked by trees and hills and valleys. Plus toting around a receiver and Yagi will be a (minor) PITA. It makes me wonder if a small quadcopter "drone", equipped w/the receiver wouldn't be less of a PITA and more effective in finding the beacon ? It wouldn't be hard to make it semi-autonomous; have it do a search pattern and hover over the target (if found). But a good quadcopter and receiver would likely be $600 - $1000.
Perhaps a better solution would be to have the arrow "puff out" some markers or marking paint at fixed intervals, to better aid in tracking the trail ?
Or some other "odd" solution. I don't know. Coming up with a semi-foolproof answer that's light and small enough, let alone cheap enough, is not an easy task.