Two Players
For two people there is a simple solution which is commonly employed. This is the so-called divide and choose method. One person divides the resource into what they believe are equal halves, and the other person chooses the "half" they prefer. Thus, the person making the division has an incentive to divide as fairly as possible: for if they do not, they will likely receive an undesirable portion. This solution gives a proportional and envy-free division.
The article on divide and choose describes why the procedure is not equitable. More complex procedures like the adjusted winner procedure are designed to cope with indivisible goods and to be more equitable in a practical context.
Austin's moving-knife procedure gives an exact division for two players. The first player places two knives over the cake such that one knife is at the left side of the cake, and one is further right; half of the cake lies between the knives. He then moves the knives right, always ensuring there is half the cake – by his valuation – between the knives. If he reaches the right side of the cake, the leftmost knife must be where the rightmost knife started off. The second player stops the knives when he thinks there is half the cake between the knives. There will always be a point at which this happens, because of the intermediate value theorem.
The surplus procedure (SP) achieves a form of equitability called proportional equitability. This procedure is strategy proof and can be generalized to more than two people.
Read more about this topic: Fair Division
Famous quotes containing the word players:
“The players have often mentioned it as an honour to Shakespeare, that in his writing, whatsoever he penned, he never blotted out [a] line. My answer hath been, “Would he had blotted a thousand.””
—Ben Jonson (c. 1572–1637)
“Yeah, percentage players die broke too, don’t they, Bert?”
—Sydney Carroll, U.S. screenwriter, and Robert Rossen. Eddie Felson (Paul Newman)