1. If you are one of the few highly ranked players still playing and you play a lower ranked player, you gain virtually nothing for winning, but a drop a lot for losing.

2. Therefore, all high level playing does is risk your rank.

3. Therefore, you are inclined to stop playing.

4. Whereupon the number of highly ranked players still playing decreases, and with it the odds of fighting one.

Conclusion: There has to be an incentive for highly ranked players to play lowly ranked players, or there won't BE highly ranked players.

The simplest solution, I think, is to make it so that if players do not play games often enough, they automatically lose rank.  This rapidly eliminates inactive but elite players from the leaderboards, which causes active but weak players to rise upwards, which then increases the odds that active but elite players will fight games that have good returns.  In the mean time, they have the incentive to play now and then or lose their rank.

I think it would work something like this:

4-7 days of inactivity: 1 rank per day

8-14 days of inactivity: 2 ranks per day

15-21 days of inactivity: 3 ranks per day

and so on.  This would act as a strong and permanent leaderboard wipe effect.