Catalogue of simple, illustrative game theory games

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Can anyone point me to a catalogue of well-known illustrative game theory models? I'm particularly interested in two-player competitive games. I've searched a bit and found this page that lists normal-form games implemented in a particular package, which covers a lot of the very common ones (prisoner's dilemma, stag hunt, chicken).

I'd like to use these to build my game-theoretic intuition. And I'm interested in part because of a toy model I've been playing with; I'm curious if there's anything written up about it or about similar games, but I don't know what it would be called in the literature.