Agent Models Problems

Last problem was 0480 (HELP)

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Q164. Sketch a flowchart that represents the logic of setting up a Schelling "tipping model":

To Create Schelling Model

1. Set up the model.
2. Run the model until everyone is content to stay where they are.

To Set Up

1. Start with an NxN grid.
2. Identify a number of type A residents and a number of type B residents such that A+B is less than N².
3. Randomly place As and Bs on grid.

To Run the Model

1. For each resident, evaluate move/stay choices
2. For each resident, find new location for all those that choose move.

To Evaluate choice

1. Identify the resident
2. Count all neighbors
3. Count similars
4. Compute ratio
5. If larger than threshold, mark as stay, otherwise mark as move

To Move

1. Select a random square
2. If empty, move there. Otherwise try again.

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Q165. What's the difference between an "equation-based model" and an "agent model"? What are some other synonyms we might hear for these terms?

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Q166. Consider a one dimensional cellular automata that looks like this:

Generation 1	0	0	0	0	0	0	0	0	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0	0
Generation 2

Show what the next few generations would look like subject to "rule 93":

Rule 93
0	0	0		0	0	1		0	1	0		0	1	1		1	0	0		1	0	1		1	1	0		1	1	1
	0				1				0				1				1				1				0				1

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Q167. Suppose we have a diffusion process in which all susceptibles who are in contact with an infected in a given time period become infected in the next time period. On the grids below color in squares to indicate what happens over the first six time periods beginning with one infected. Then fill in the table and chart the data.

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Q168. Suppose we have a diffusion process in which susceptibles who are in contact with an infected in a given time period have a 50% chance of becoming infected in the next time period. Now play the “game” again except this time flip a coin each time (or use a random number chart for probabilities other than 50:50) to see whether neighbors become infected or not. Note: You might not want to play all the way out to time period 5! On the grids below color in squares to indicate what happens over the first six time periods beginning with one infected. Then fill in the table and chart the data.

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Q169. Consider the 12 block neighborhood bounded by parks on the north and south and major thoroughfares on the east and west. Green houses are supporting Obama, purple houses Romney.

Using the facing blocks delineated by the red dashed lines as units (it yields 15 of them), calculate the index of dissimilarity.

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Q170. Suppose you have a population of one hundred persons. It is divided into five categories of willingness to join a protest all of which depend on people's expectations of how many others will appear at the protest. The thresholds range from very low (I'll go if anyone else is going) to the very high (I won't go unless basically everybody else is going).

Assume the population is divided among these categories as follows:

Challenge of Recruiting	Very Easy	Easy	Average	Hard	Very Hard
Participation Threshold	1	10	40	60	99
Number at this threshold	10	20	40	20	10

a. If news reports suggest that 15 people will show up, how many actually will?

b. If last week saw participation of 41 and this is widely reported so that everyone knows, how many will come out this week? And then next week? And after that?

c. What if 91 came last week?

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Q171. A common phrase to describe processes in which people engage in imitative behavior is "bandwagon effect." Explain the appropriateness of this metaphor.

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