Agent Learning and Strategy Invasion

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**Adding Territorial Structure to the Simulation**

Note: in order to run the simulation referred to in this slide, go here, to the Java Applet version. You will be directed to download the latest version of the Java plug-in.

In the demonstration to the left we add an element of geographic structure as promised in the previous slide. This time, every given agent is no longer equally likely to connect with every other agent. Loosely speaking, the probability of a connection between agents A and B is now proportional to

`[ 1 / d(A,B) ] ^ α`

Here, d(A,B) is the distance between the agents, and α is a number that may vary from 0 to
positive infinity. We call α the *territorial structure* parameter, and use it to alter the degree
to which the agents try to connect to their closest neighbors. In fact, when we set α to 0, the
expression above reduces to 1, which means that any pairing of agents is equally probable. In this case, the
situation is reduced to that of the previous demonstration, where there are no geographic constraints on
agent connections.

On the other hand, if you set α to **5**, then a connection between two partners
distance **d** apart is **32** (i.e. 2^5) times more likely to form than that between two partners that are
distance **2d** apart. You may notice that the invasion lines become better defined, as the agents tend to
influence and learn from close neighbors, as opposed to random agents far away.

Incidentally, note that in this simulation we have decided to put the agents on a Torus, instead of just a piece of the Euclidean Plane. Imagine cutting out the square piece of canvas these agents live on, rolling it to connect the top and the bottom edges, then connecting the resulting tube into a donut. This donut is the real world the agents live on, and the picture you see to the left is simply the donut's representation on the flat screen of your monitor. Note that agents at the opposite edges of the square seem far apart, yet are actually close together on the Torus.