The D&D Gamma World book doesn’t give much advice on when to give out rewards to players, apart from experience points.

Non-experience rewards in Gamma World can be several things: a draw from an Omega Tech deck, one or more rolls on the Ancient Junk table, ammunition, or other useful items.

The D&D Essentials Rules Compendium provides a model for a reward system, and that forms the basis of the rewards table for Gamma World.

Download the Gamma World Rewards Table!