Each Christmas my wife attends a party where a bunch of suburban erstwhile party-girls get together and A) drink and B) exchange ornaments. Looking for any excuse to get invited to hang out with a bunch of drunk soccer-moms, every year I express sincere scientific interest in their peculiar mechanism of matching porcelain trinket to plastered Patricia. Alas I am denied access to their data.

So theory will have to do. Here is the game they play. Each dame brings with her an ornament wrapped in a box. The ornaments are placed on a table and the ladies are randomly ordered. The first mover steps to the table, selects an ornament and unboxes it. The next in line has a choice. She can steal the ornament held by her predecessor or she can select a new box and open it. If she steals, then #1 opens another box from the table. This concludes round 2.

Lady #N has a similar choice. She can steal any of the ornaments currently held by Ladies 1 through N-1 or open a new box. Anyone whose ornament is stolen can steal another ornament (she cannot take back the one just taken from her) or return to the table. Round N ends when someone chooses to take a new box rather than steal.

The game continues until all of the boxes have been taken from the table. There is one special rule: if someone steals the same ornament on 3 different occasions (because it has been stolen from her in the interim) then she keeps that ornament and leaves the market (to devote her full attention to the eggnogg.)

Theoretical questions:

  1. Does this mechanism produce a Pareto efficient allocation?
  2. Since this is a perfect-information game (with chance moves) it can be solved by backward induction. What is the optimal strategy?
  3. How can this possibly be more fun than quarters?