Combined Assignments 5 and 6. Due by midnight, Wednesday April 13, 2022. Professor Epstein
Indicate every solution by Part and Letter. So the first problem is labeled Part 1 (a), etc.
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Part 1. Sugarscape Problem
Open 2020JScape2peak. Leaving all other settings as given there.
(a) Expand the world to 32 X 32. Increase the population to 1000. Add a third peak centered at (-15, 15). Set up the turtles so that initially, they occupy random positions to the left of pxcor = -15. Their y-coordinates (pycors) stay random as before. Show your Setup code and a screen shot of this initial configuration.
(b) True or False? With Instant growback, turtles make it to all three peaks. That is, no peaks remain unoccupied. Is that true or false? Show a screen shot. Explain the result.
Part 2. Lanchester Combat with Breakpoints
In combat, a force ceases to function when their numbers sink below their “breakpoint,” which is some fraction of their initial value. If the breakpoint is zero, they are unbreakable. If it is 0.7, then the instant they suffer 30 percent attrition of the initial force, they become completely inoperable. Effectively, their level drops immediately to zero. To explore this Open LanchesterTheory. Modify and run only the goSquare routine as follows:
(a) Make two new interface sliders called blue-breakpoint and red-breakpoint that range from 0 to 1 in increments of 0.01.
(b) Modify the Code so that Red and Blue forces are set to 0 if they sink below the product of their breakpoint and their initial force. Submit your code.
(c) Set both breakpoints to zero and submit a plot of the run (it should match the existing goSquare plot showing a fight to the finish stalemate
(d) Set both breakpoints to 0.20 and submit a plot of the run. Why, if they have the same breakpoints do we not get the same stalemate result?
(e) Set Blue’s breakpoint back to zero and Red’s to 0.50. Show and explain a plot of the result.
Part 3. Game Theory
Some hold that best way to maximize the public good (the sum of all payoffs) is for each individual to maximize their self-interest, regardless of the strategic setting. One such setting is shown in the Prisoners’ Dilemma payoff matrix below, where “Arm” and “Disarm” stand for Defect and Cooperate generally.
(a) Carefully explain whether rational individuals will Arm or Disarm given the payoff matrix above.
(b) Would they be collectively better off (would the sum of payoffs be higher) if both behaved “irrationally?”
(c) Suppose you want to induce mutual disarmament. One might imagine that the way to do this is to dramatically increase the payoffs to disarming, as in the game matrix below.
Will that work? Does this make it rational to disarm?
Open the NetLogo ClassDemographicGames. Upon setup, the interface should look like this:
Using exactly the settings shown, compare two movement modes, using the movement Chooser in the upper left.
(a) Select the Mixed movement mode, indicating perfect mixing, with agents moving to random sites each time they are activated. Standard (expected value) models predict that the defector population will grow until it occupies the whole landscape. Is that what happens here? What does happen and why? Use the slider at the top of the Netlogo page (above the ticks counter), to slow the model down so you can see what’s going on sequentially.
(b) Select the Fixed movement mode. Now what happens and why?
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