Access and the Winner-Take-All Market

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**Increasing Access can Increase Connection Probability**

We now try to examine more precisely what effect access has on the connections agents form. At first, we begin with the simple case that there are no constraints on the number of channels available. Channel count, C, is infinite.

First we rank the agents from the most knowledgable to the least knowledgeable. Then for each agent, we consider what the probability is that another agent will want to connect to her. With infinite channel count, this problem is easy. The probabilities are plotted in the graph, below.

Access increases from bottom to top and the agent's rank increases (worsens) from left to right. For a given agent and level of access, the height indicates the probability that the agent appears in the top C choices of any other agent. So, as access increases, the probability of being able to reach any given agent climbs to one.

The agents we created before, however, actually have a limitation of only two channels. This affects the partnerships that form with universal access. When everyone can reach everyone else, which networks actually form? If C represents the number of channels you have, the new question becomes "What are the chances that the agents you can reach are among your top C choices?" You can only talk to at most C others at once.

Go on to the next slide to see what happens.

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