What is "math"? and what is it "for"

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What is "math"? and what is it "for"
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(High school) algebra is a set of definitions for working with equations - these equations apply to anything that can be counted or

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measured

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mechanism design

A mechanism has several parts: - uncertainty that managers know (or can learn), but stockholders

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won't (until too late)

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Network economics

Simple network economics: "the cloud"

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Simple network economics: "the cloud"
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Homework

Write an email, send to ises-hw@turnbull.sk.tsukuba.ac.jp. Subject is "ISES Network Homework".

  1. Give one network you are connected to (not the phone company, not the Internet, and not Microsoft Office).
  2. Does your u(N) have decreasing, increasing, or constant returns to N?

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3. What is the cost of connecting to the network? (In English...)

Modern network economics

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  • Being on the "shortest path" can give power

There are also global parameters of a network, that sometimes have surprising properties

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  • Diameter of the whole network
  • Diameter of a circle: goes through the center, connecting two points on the circle - but networks may not have a well-defined center
  • Diameter of a circle is the longest line segment that intersects the circle
  • Define the diameter of a network as the longest "shortest path" connecting any two members of the network
  • Useful fact: a random link will reduce the diameter of a "sparse" network dramatically.