I believe on the worldly point of view, yes, Tibet is certainly a pawn not just for India and China but for Western powers as well. So long as there are still values in Tibet as a pawn, it will remain so. But for the Western power like the US, Tibet is fast loosing its value versus the what can be gained from China. Hence, recently, President Obama has stated clearly that Tibet is part of China.
India on the other hand is caught between a rock and a hard place because India has hosted the Tibetan exile community and the Tibetan "government" including the Daiai Lama and since Tibet/China is just across from India, the threat to India is perennial. India is loosing its economic race with China by a long way and has its own internal issues with its weak political system and an unstable government resulting from it, security threats from Pakistan and from its huge population of the poor.
Hence, in my opinion, India is loosing the pawn (Tibet) it has captured; not physically, but in its value. In other words this pawn is being phased out by China through acceptance of Tibet to be part of China by the rest of the world.
