(Repost of something I did at the Protein Wisdom Pub a little while ago.)

A games theorist thinks up content-free games and plays them (or simulates playing them on a computer) as a way to help think about reality. Because the games are content-free, they avoid distracting elements like ethics and morality; in the best case they end up demonstrating why things like ethics and morality came to exist in the first place.

Sometimes the results can be a little surprising, especially when something very simple turns out to have profound implications. For instance, it’s fairly obvious that John McCain isn’t up to speed on recent games theory as regard the game called “Prisoner’s Dilemma”.

In my ever-continuing effort to divert my attention from the fact that I’m going down the tubes, I present to you my tentative contribution to the world of content-free games. I call it “Centralization”.  Here is the game board:
Centralization Game Board

The number of divisions of the outer annulus is variable according to taste; the minimum is two. The innermost circle is called “Boss”; the divisions of the outer ring are “Subordinates.” You will need, in addition to the board, a single die or other random-number generator and a supply of counters or chips. The counters are called “problems”. What makes it “content-free” is that we don’t specify what the problems are, we simply allow them to exist.

With any content-free game, what is most important is the rules. Centralization has several sets of rules, depending on what it is you are trying to model. The basic game is as follows:

A. The Problem Phase — For Each Zone:

  1. Roll the die
  2. Place the resulting number of counters in that zone

B. The Solution Phase — For Each Zone:

  1. Roll the die again
  2. Remove the resulting number of counters from that zone

Repeat many, many times. The goal of the game is to keep the board as clear of “problems” as possible.

Not too interesting, is it? On the average, over many rounds, the game board will be clear at the end of step 2 of the Solution Phase. That won’t prevent the occurrence of runs, in which one zone accumulates counters that aren’t cleared away by the clearing roll, but over many trials it will (or should) average out.

For something slightly more interesting, at the end of the Problem Phase, push any counters in the “Subordinate” ring into the central zone. In the Solution Phase you then only have to roll the die once, for the central zone. But that’s a problem, isn’t it? On the average over many trials, you add ten and a half “problems” to the central zone (fourteen, if the “Boss” is allowed to have its own “problems”) but only remove three and a half in the solution phase. You’re going to need a lot of counters… I call this version “Tyranny”.

Note that it doesn’t matter why all the problems get pushed to the middle. This is another way it’s a content-free game.

You are now invited to propose rule-sets that make the game different, keeping the overall goal (a board as clear of “problems” as possible). The only ones I’ve been able to come up with that match or improve the basic game are “Angels in the Center”, a modification of “Tyranny” in which you roll the die for the center space as many times as there are zones on the board — that is, the Boss must be preternaturally capable — and “Manager”, in which any counters remaining in the outer ring after the solution phase are pushed to the center, but you roll twice for the Boss’s “Solutions” — that is, the central controller is somewhat more capable than the subordinates. That last one has the effect of minimizing “runs” in the outer ring. Analogies should occur to you.

I’ve discovered several rule-sets that make it worse, though few as bad as “Tyranny”. One is “Bureaucracy”, in which each Subordinate zone is required to roll for the number of “problems” that can be pushed to the center; another is “Favoritism”, in which one Subordinate zone is allowed to push “problems” into the other two. You may find others. Discuss.

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