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You have three children: Angela, Beatrice, and Caroline

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You have three children: Angela, Beatrice, and Caroline. You come home one night to find a lamp broken in the living room. You know that one of your children broke it, but don't know which one. To figure this out you make them announce their claim ("I broke it" or "I didn't") one-by-one, with each of them present. First you ask Angela. Then after everyone hears Angela's response you ask Beatrice. Then Caroline.
If at least one child claims to have broken the lamp then you will give the children who claim to have broken the lamp €2 (their normal allowance) and give the other children €5. If none of the children claim to have broken the lamp, none of them get any money. Draw out the game tree and determine the backwards induction equilibrium. Does it matter in what order you ask them?