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In the world of Pokemon, your partners' progression depends almost completely on it's level. As you are probably familiar, many of the moves that your Pokemon can learn, and in most cases when it evolves into a stronger form are determined by your Pokemon's level.
Proposed System:
Regardless of the number level, it takes a Pokemon 100 EXP to level up. After a battle with a Pokemon, any Pokemon involved will gain experience based on how the level of the Pokemon defeated compares to their own.
For frame of reference, a Pokemon that is within 3 levels above or below your Pokemon's level, it is considered a good challenge, and will award 20 EXP upon its defeat. Due to Trainer's Pokemon being stronger, if you defeat a Pokemon within this threshold which belongs to a trainer, you will get twice the experience, earning a total of 30 EXP. Should one defeat a Gym Leader's "Prized" Pokemon, or a "Boss Pokemon" a full 100 EXP will be given.
The table below describes how Pokemon of different levels will compare to you, as designated by Challenge Thresholds. These challenge thresholds will not only determine how difficult it should be defeat your opponent from an RP standpoint, but how much EXP is rewarded upon it's defeat. A Pokemon weaker than yours will provide less experience, and a Pokemon stronger than yours will provide more.
Please note, that in order to take into account that players may battle each other, all EXP rewards are given AFTER a battle, regardless if the trainer is victorious or not.
If these numbers make the game feel too grindy, I will increase the experience rewards accordingly.
*Edit, 8/17/2016, numbers significantly increased