It looks like you have exclusively D2 teams, so the prestige difference is negligible. Simply spend your money wisely so that you exert more recruiting effort on said player. Some thoughts to consider:
1. Did you start with more money? Be really clear on how much the person you're battling has in the bank (make especially sure that they had to recruit at least one freshman the previous year and didn't roll over 100% of their funds!!).
2. Check the distance of your opponent from the player, find a similar player, and note the differences in costs. This will tell you how much money your opponent loses by matching one of your actions.
3. Check your opponent's other recruits. Are there any other battles that might force him to veer off one player or the other? How close are your opponent's other recruits to his campus? How many states are they from? These are all tells that allow you to adjust and modify your guess on how much money he can spend still.
4. Beyond that, just spend wisely (HVs vs. CVs based on your distance, minutes promises if you're in a position to make them, etc.). You're playing a game of chicken -- be willing to play it all the way or at least have a point where you're willing to veer off if something indicates your guess was wrong regarding how much money your foe has.