Agent Strategies

Strategies for the agents in these games are pretty simple to understand.

Imagine a string of 0s and 1s.

00101100

A Strategy would look at the last M (for memory) digits in this string. Lets set M = 2 for right now. A strategy would consist of a resonse to all possible 2 digit strings. For example:

00 -> 1
01 -> 1
10 -> 0
11 -> 1

So for the string given earlier, this strategy's response would be 1.

For M = 2, there are 16 possible strategies. For any M, there are 2^(2^M) strategies. This number gets large very quickly, you can see. Typically, I use M =3, so there will be 256 strategies available in the game. For M = 4, there are 65536 strategies.

Each agent will choose S strategies at the beginning of the game and use the most successful strategy of these strategies over the last N time steps. Usually, S will be 2 or 3, but might be higher. In the Minority Game paper, using more than 5-6 strategies didn't improve the performance of the game. In the Lamper paper, they used S=2, so each agent had 2 strategies available to use.

Note that each agent uses the most successful strategy of their available strategies. They (or someone!) keep a running total of how well their strategies have performed over the last X number of turns and choose the most successful of their strategies to use for the next step.