Your calculations look right for Shapley Values. I was calculating based on Ninety-Three’s proposal (see here). So it’s good that in your calculations the sum of parts equals the combined, that’s what we’d expect for Shapley Values.
Doh! Thanks for the clarification. I see I misunderstood you targeting Ninety-Three’s proposal about locking in a “more work” ratio.
For me, locking in the ratio of solo profits intuitively feels unfair, and would not be a deal I’d agree to. Translating feeling to words, my personally-intuitive Alice (A) and Bethany (B) story would go:
Alice is a trained watchmaker, Bethany makes robots. They both go into the business of watch-making.
Alone, Alice pulls in $10,000/day. Expensive watches, but very slow to make.
Alone, Bethany pulls a meer $150/day. Cheapo ones, but she can produce tons!
Together, with Alice’s expertise + Bethany’s robot automation, they make $150,000/day!
Alone, neither is able to compensate for their weakness: Alice’s is production speed, Bethany’s being quality. The magic from their synergy comes from their individual weaknesses being overwritten by the other’s strengths. Value added is a completely separate entity versus the ratio of their solo efforts; it simply does not exist unless they partner up. Hence, I must treat it separately and that difference in total value vs. the sum of their individual efforts rightfully should be divided equally.
The value/cost of doing business w/ others, perhaps?
I’m just learning this, please forgive me if I’m misunderstanding. I’m calculating your example differently though:
Day 1: (200 + (400-200-0)/2) = 300 to A (0 + (400-200-0)/2) = 100 to B
Day 2: (100 + (200-100-100)/2) = 100 to A (100 + (200-100-100)/2) = 100 to B
Day 1+2: (300 + (600-300-100)/2) = 400 to A (100 + (600-300-100)/2) = 200 to A
300+100 does equal 400, 100+100 does equal 200
Sum of parts does equal the combined?
Your calculations look right for Shapley Values. I was calculating based on Ninety-Three’s proposal (see here). So it’s good that in your calculations the sum of parts equals the combined, that’s what we’d expect for Shapley Values.
Doh! Thanks for the clarification. I see I misunderstood you targeting Ninety-Three’s proposal about locking in a “more work” ratio.
For me, locking in the ratio of solo profits intuitively feels unfair, and would not be a deal I’d agree to. Translating feeling to words, my personally-intuitive Alice (A) and Bethany (B) story would go:
Alice is a trained watchmaker, Bethany makes robots. They both go into the business of watch-making.
Alone, Alice pulls in $10,000/day. Expensive watches, but very slow to make.
Alone, Bethany pulls a meer $150/day. Cheapo ones, but she can produce tons!
Together, with Alice’s expertise + Bethany’s robot automation, they make $150,000/day!
Alone, neither is able to compensate for their weakness: Alice’s is production speed, Bethany’s being quality. The magic from their synergy comes from their individual weaknesses being overwritten by the other’s strengths. Value added is a completely separate entity versus the ratio of their solo efforts; it simply does not exist unless they partner up. Hence, I must treat it separately and that difference in total value vs. the sum of their individual efforts rightfully should be divided equally.
The value/cost of doing business w/ others, perhaps?