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In chess there is a fairly common situation where you are in first place in the last round of a tournament, 1/2 of a point ahead of your opponent (you get 1 point for winning a game and 1/2 point for a draw). So if you win or draw the game, you win the tournament and get a lot of money. If you lose the game, your opponent wins the tournament and gets the money. You get 2nd place, i.e. less money possibly split with other competitors.
That means you can choose a safe playing strategy that likely leads to a draw, while your opponent has to choose a risky strategy with higher chances of winning.
(Some chess context: high level games are usually drawn. They are only won by someone making a mistake. Also, the first move (white pieces) confers an advantage, so it's usual to seek winning opportunities if you have white, while just trying to hold the draw if you have black. To attempt winning with black requires seriously risky play. Bobby Fischer basically conquered chess in the 1960's by constantly trying to do that, which required playing with maniacal intensity all the time).
Definitely the most interesting comment here. Thanks.
I get that but, no matter their strategy, aren't they still competing against one another for the same resources: a (better) ranking in the leaderboard?
Maybe I have to go to the bathroom and I see a janitor making their way towards the same bathroom. We both start an all out sprint for the bathroom door. In this moment we are both adversaries, but his goal is to clean and my goal is to evacuate my bowels. Sure we are competing for the same resource, the bathroom, but our objectives with the bathroom are different. You could also say we are almost playing a different game, he's trying to not spill his mop bucket and I'm clenching my cheeks.
But those are just different debuffs!