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Ways to make a cooperative King of the Hill contest

I generally think of [King of the Hill contests](https://codegolf.codidact.com/categories/46/tags/4366) as inherently competitive. However, I wonder if there is a way to have a contest that rewards cooperation. I would still want to see a leaderboard, with answers competing to get the highest on that leaderboard. In some sense, the answer at the top of the leaderboard would be the "most cooperative".

I'm not looking for ideas for specific games (those can be posted to the [Sandbox](https://codegolf.codidact.com/categories/50)). I'd like to see suggestions of general approaches that could be used across many games. This could be a way of measuring cooperation in an otherwise competitive game, or ideas for categories of game that allow cooperation to be part of the goal, while still allowing individual scoring for a leaderboard.

I don't have a preference on whether all answers compete at once in a single arena, or whether small groups of a fixed size are selected at random and scored based on their outcomes over many such games.

My measure of whether a suggestion fits here would be whether it results in contests where the main aim of an answerer is to cooperate towards some goal.