# Dividing 6 Stones

Six stones, shown in the middle row, are to be divided between two players, Ann and Beth. The values Ann and Beth assign to the stones are shown above, respectively below the stones. In the "00" version, Ann's and Beth's values add up to 100, in the "0000" version they add up to 10000. The upper (initially empty) row shows stones that Ann got, and the lower row shows stones Beth got.

Values are created (randomly) by clicking the buttons "random00" respectively "random0000" (for the two versions explained above. But you can also input 12 numbers into the values fields and click the "read0000" or "read0000" button. The values are automatically rescaled for the two versions. You can also choose 3 sets of predefined values with the other three buttons.

Below the outer box, possible distributions that optimize three features for the present data are shown. Distributions are abbreviated by lower case strings like "aababa", indicating that Ann gets the first, second, fourth and sixth stone, counted from left, and Beth gets the other two.

On the left, the red background indicates the player who is supposed to take the next stone from the middle row. This can be changed by clicking the corresponding "chooses" button, but when playing a game, this is taken care of automatically. A stone is taken by clicking on it. Clicking on a stone in Ann's or Beth's row, the stone goes back to the middle row. The sums of the stone's values for Ann and Beth they presently have---their "satisfactions"--- are shown as "total".

You can play one of the three games "ABABAB", "ABBABA", or "ABBAAB" by clicking these buttons. If the player supposed to move needs a hint from the (clever) computer, click the "hint" button to the left. If you want to play again with the same values, click the game buttons ("ABABAB" ...) again.

After having played a game, or distributed the stones manually, you can compare the features achieved with your distribution to the optimal ones outside the inner box but inside the outer box. In addition to the three features "sum of satisfaction", "difference of satisfaction", and minimum satisfaction, you can also see if the distribution is envy-free, or if it is Parteo-optimal, and if not, which distribution Pareto-dominates ours.

Game played:

 Ann: total: Ann's values Beth's values Beth: total:
 sum of satisfaction difference of satisfaction minimum satisfaction dom. by
 possible possible possible sum of satisfaction difference of satisfaction minimum satisfaction

Erich Prisner