3) Each of the other heirs withdraws from the kitty 1/n of his or her bid.4) The money remaining in the kitty is divided equally among the n heirs.

Bob, Carol, and Ted will get pieces X, Y, and Z of cake. If Bob cuts the cake, Carol “approves” of piece Y, and Ted “approves” of piece Z, then there is no problem.If Carol and Ted only approve of piece X, then X and Y are rejoined for Carol and Ted to divide and choose while Bob gets piece Z.

If the players provided each other with their preferences before taking turns divvying them up, both could use the strategy simultaneously.

The strategy is as follows for each player:

Complete a table representing choices at each turn by alternating filling in a player’s last choice with the other’s least preference starting with whichever player chooses last and working backwards to whichever goes first.

Bob: House Carol: Investments

Bob: Pension Carol: Vehicles

In a sense, Bob played insincerely (because he did not pick according to his real preferences) but by doing this he actually did better according to those preferences: he ended up with his first two choices instead of his first and third as he would have by playing sincerely.