3 ms·

Luckily, this is a solved problem in economics. You use the Shapley Value (https://en.wikipedia.org/wiki/Shapley_value https://en.wikipedia.org/wiki/Shapley_val

Luckily, this is a solved problem in economics. You use the Shapley Value (https://en.wikipedia.org/wiki/Shapley_value https://en.wikipedia.org/wiki/Shapley_value) of each contributor. For small groups, you can use http://shapleyvalue.com/index.php 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.

robocat 4y ago
This problem occurs exactly when founding a business - how do you apportion equity ownership when one central founder is essential, and co-founders have a multiplier effect on profitability? How do you deal with the uncertainty in the multiplier, or the future measurement of the multiplier? 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.
- lalaithion 4y ago
  Right, this is why Shapley value is not the market value. 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.

robocat 4y ago

This problem occurs exactly when founding a business - how do you apportion equity ownership when one central founder is essential, and co-founders have a multiplier effect on profitability? How do you deal with the uncertainty in the multiplier, or the future measurement of the multiplier? 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.

lalaithion 4y ago
Right, this is why Shapley value is not the market value. 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.