Infrequently updated
musings vaguely inspired by my PhD project.
At Danish Christmas get-togethers the package game is often played. Here are some reflections based on recent personal experience. Disclaimer: None of this is to say that my family does not consist of genuinely altruistic warm-hearted Christmas-spirited über-philanthropists.
Rules: Each player brings a package (of some pre-arranged monetary value, say $3) which is placed in a package pool of un-owned packages. In the game’s first phase players take turns rolling a dice, each 6 rolled enables the player to take one package from the pool. When the pool is empty the game shifts to phase two in which a 6 lets a player take any package owned by another player. Usually, one person sets an alarm clock to a setting within a certain announced interval (e.g. 15-25 minutes). When the alarm sounds, the game is over and everybody keeps his or her then-current presents.
Of course, if the clock-setter is also a player, this creates a slight unbalance as one player is privy to special information about the game state.
So, what can we say about the game dynamics etc.
- Technically, this is a zero-sum game. The sum is fixed (number of packages).
- There are (technically) incentives to cooperate. For instance, in a player group of 10, 5 might agree never to “steal” from one another. Unless the rest catch on, anyone on the ally side will then only be potentially victimized by 5 players, while any non-ally will have 9 enemies.
Less than full-blown pre-game conspiracy will do. In the logic of Tit-for-Tat any player may (at a short-term cost) communicate his or her vengefulness by always reciprocating an attack – the message may be clearest if the person consistently steals the present that the other player stole from him or her most recently. However, this strategy works poorly against itself and the trick is of course when to quit if caught up in a disastrous series of mutual retaliation (hey, I take my package game seriously). - The game has negative feedback (there's a push towards an equality equilibrium) due to the norm (see below) that you should generally steal packages from those who have many.
A number of social norms seem to apply in the games I’ve participated in:
- You don’t steal packages from small children (unless they have huge numbers of packages)
- You should not steal packages from the very package-poor (players generally scan the table for the larger piles and steal from them)
- 'You don’t steal from extremely close family (your own children, your spouse). Alternative phrasing: You don’t steal from those with whom you will be next to you on the car ride home. Alternative 2: You consider packages taken by members of your household as partly yours since they’ll be under your roof (i.e. the value of taking such a package is less than 1 since you’re partly stealing from yourself).
[More to come as field work progresses]
posted by Jonas Heide Smith # 8.12.04
