For small groups, you can use http://shapleyvalue.com/index.php, and for the example you gave above, A should get 233k of the total 400k value, and the other two should get 83k of the total 400k value.
For small groups, you can use http://shapleyvalue.com/index.php, and for the example you gave above, A should get 233k of the total 400k value, and the other two should get 83k of the total 400k value.
The Shapley Value seems like a perfectly spherical moose optimum. A can create an annual profit of 100k, and A+B+C can create a profit 400k. A will only bring on B or C if A can get more than 100k.
Let us assume B is currently working in Chile and they would accept 40k (better than their current pay), and C works in the US and 120k is their minimum acceptable payoff to change jobs. The potential groups are:
* option X: A profit 100k
* option Y: A+B profit 200k, and A+B could argue over how to split the 60k excess.
* option Z: A+B+C profit 400k, and A+B+C could argue over how to split a 140k excess.
Or A just starts the business and keeps 100% ownership, and A offers B 40k, and offers C 120k, and A pays themselves 240k and A also gets 100% of the market value of the business. B + C complain that’s unfair, but accept the jobs anyway.
One could also imagine a world in which A is a software engineer who can make 100k at his day job, but B and C are experts in a little-known, poorly paying, field with the potential to revolutionize the world, and they’re looking for a software engineer to help them build a product. B and C can then offer A 110k, while each pocketing 145k.
Also note that the scenario above is not the scenario I worked out in my original post. If the software engineer makes 120k and the Chilean makes 20k on their own, then the Shapley value is actually
A = 166k
B = 86k
C = 146k
Shapley value != market value, but in many cases, it’s usually fairer than market value.