TASK DEFINITION: Given a negotiation between two participants, answer 'Yes' if both participants agree to the deal, otherwise answer 'No'.
PROBLEM: THEM: how about you take the hat and balls and i will take the books? YOU: i can't accept that deal. if i can have the books you can have the hat and the balls... would that work for you? THEM: the books are the only things of value to me YOU: same as me. the only other deal i would be willing to make is if we can split the difference and i can have one of each THEM: okay can i have 1 book and the balls? YOU: you can have one ball and the book THEM: deal YOU: okay thank you!

SOLUTION: Yes

PROBLEM: THEM: if i can have the hats you can have everything else YOU: that works for me THEM: okay great! thank you!

SOLUTION: Yes

PROBLEM: THEM: i would like one of everything YOU: i would like just the hat THEM: the hat is something i need or we won't be able to make an agreement YOU: hmmmm. same with me. THEM: is there any way you can make this work without taking the hat? YOU: hat is all i need THEM: i'm going to get shafted here but i'd rather meet an agreement then not.

SOLUTION:
Yes