|
Game theory - A Tutorial |
|
Cooperative: Shapley Value |
|
How should a farm owner, Bob, split revenues with his two workers? Without workers, Bob cannot produce any revenues; with one worker (W1 or W2), he can produce $100.00, With two workers (W1 and W2), he can produce $200.00. The workers cannot work without Bob. How should Bob and his workers share the $200.00 revenues when they work together? Shapley argues as follows. Imagine that the workers and Bob show up in a random order and let us see how much each adds to the revenues, on average. That should be that person’s share. If they arrive in the order (W1, B, W2), then W1 adds 0 (he cannot work without Bob), Bob adds 100 because that is how much he can produce with W1 and W2 adds another 100 because together they can produce 200. Averaging over the 6 equally likely orders, we find that Bob should get $100.00 and each worker $50.00. See [2] for more details. |
