With a little work, by constructing the player’s ordinal preferences, you can show that the structure of this game is very similar to a 2 person dilemma – which is certainly not obvious.

Label the outcomes, from the top node to the bottom node, O1, O2, and O3.

Then,

C: O2 > O3 > O1

And arguably,

L: O1 > O2 > O3

But because of the strategic nature of the tree, the parties should end up at O3, which is dominated by O2. This is a particular problem for reasonable agents who want to ignore the past bad history of C’s.

(O3 could be justified if L’s preferences were completely opposite: O1 > O3 > O2, but then L has little hope in convincing C that she has an unconditional preference C trying to kick the ball.)

I have done a brief review of the Peanuts cartoons on this football theme, and counted 8 different excuses Lucy comes up with after the fact to explain away her purported commitment to O2 over O3 – that she would rather see Charlie try than not try to kick the football.

One theme that continually emerged was L’s insistence that C didn’t trust her, and C would feel bad, try to kick the ball and be disappointed again.

L’s one line I liked was “Never trust a woman’s tears”, as her explanation of why she wasn’t really committed to O2 over O3 or O2 over O1,