Together the cost from Alice to Bob’s place is $12 and if they go Separately, Alice will pay $6 and Bob will pay $11.
$6 + $6 = $12 (together)
$6 + $11 = $17(separate)
The pie is $17 - $12 = $5 the pie is split =
A = $6 - $2.50 = $3.50
B = $11 - $2.50 = $8.50
A = (trip if A went along) - (the split pie)
B = (trip if Bwent alone) - (the split pie)
Cost to A + B: $12
Cost to B: $11
Detour = $12 - $11 = $1
Pays $3 +$.50 = $3.50
Pays $12 - $3.50 = $8.50
A = (Alice’s split ride home) + (the split pie)
B= (The price start to A to B) - (Alice’s split ride home + the split pie)
Separate 6+ 11 + 18 = $32
Together: $6 + $6 +$6 = -$18
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$14
Take Alice and Bob
Possible orders: 1) Alice Bob 3) Bob Alice
Alice ½($6 + $1) = $3.50
Bob ½($6 + $11) = $8.50
Alice = ½((half the cab ride home) + ((total of start to A to B) - (B’s iindividual ride home)
Bob = ½(half the cab ride to A) + (the trip home if went separately)).
If you notice all three equations of the above are equal to $3.50 and $8.50
We will use the Shapley Value:
ABC
ACB
A = $6 B = ? C = $11 (What is B? Total cab fare: $18) B = $18 - ($6 + $11) = $1
A to C to B is equal to $17 now from A to B to C is equal to $18, now B only has to pay $1.
Now comes the Shapley value
CBA
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