This definitely doesn’t work.
For example, let’s take MTG tournaments. In one tournament, the Singapore Grand Prix Qualifiers, only the top 3 players would be allowed to play. What happened? Two of the top 3 actually conceeded the match to their opponents, who weren’t even their close friends. Why? Because these 2 players simply didn’t have the time to go to Singapore. Instead of being “dog in a manger” they simply let the other guy win. The other guy, presumably, had some sort of compensation.
If a plane ticket were the prize, then likely if there was one player who can’t make it (due to, say, school) it is likely that he’ll just give the opponent the win and receive something else in return. it’s only when both player A and B want the prize so much will they not come to some sort of agreement – even then, the prize would still be likely be split. For example, winner gets $1million. Loser gets nothing. If you were in that position, wouldn’t you want to split the money instead of risking not taking anything home? $500K is still a lot of moola. On the other end of the spectrum, winner get $10. Opponent, a good friend, offers to split it. This isn’t so much about money as it is about pride. Would you risk your friendship over $10? likely, you and your friend will still play, then probably use the $10 to get both of you drinks later.
You simply cannot use an undivisible prize as an incentive. And the bigger the prize, the more likely you’ll find people splitting it, while the smaller the prize people will be less likely to willing to risk friendships.
There is no solution to this, other than to have the skill to actually win at tournaments, then be willing to risk taking home nothing and friendships for the sake of pleasing the crowd.
(If anyone is wondering why I’m vocal on this topic, collusions always occur in Magic The Gathering, which I join weekly tournaments of. It simply can’t be avoided, and is in fact considered an acceptable strategy in the last round of the semi-finals – I’ve seen up to 6 out of 8 people draw their way into the top 8 slots, then the top 8 players divvy up the prize. Other than suspending/banning players caught doing it, there is no way to prevent players from intentionally drawing or losing if they want to. And even then, they can always do it before the tournament.)