It seems that the criteria for the prizes and awards should be well-defined according to what elements, ideas, and qualities are most highly valued in literary work.
If the award criteria are clearly defined, then work from any culture or country could conceivably win, provided the work meets the criteria for the prize.
This is not, apparently, the case for the uber-prestigious Nobel Prize which awards a medal and a monetary prize each year to a writer for a "significant contribution" to culture through literature. In fact, the Nobel website does not offer criteria as specific as "siginificant contribution" in its description of the award and so seems open to biased and arbitrary reckoning when considering deserving recipients.
One answer then is to create clear criteria for each prize or award and strive to shape those criteria in such a way that avoids geographical or culture-specific bais.