Homework 4



Homework 4: Due by the end of the term


  1. Write a brief response to the paper we read by Helmrich. Do not summarize the paper; assume your audience has read it. This shouldn't be a well-polished essay, but it shouldn't be a rambling journal entry, either. Don't try to respond to the all the arguments, just pick one or two and explore them. If you're stuck for what to write on, I suggest picking one particularly provocative passage or paragraph and analyzing it carefully and critically. Your response should be one to two pages.

  2. Problem 2.6, page 99, from Understanding Nonlinear Dynamics, on reserve in the library.

  3. For each of the following elementary one-dimensional CAs, sketch thirty time steps. In class we started with a random initial condition. For this exercises, start with a single 1 (i.e. a dark square) and a background of all 0's (all light). Do these on graph paper.
    1. Rule 2
    2. Rule 126 (does the shape look familiar?)
    3. Rule 109
    4. A rule of your choosing.

  4. As we'll discuss in class, game theory is used to model strategic interaction. Come up with some situation that can be formulated as a two-player game. Explain the different player's strategies and their payoffs.

  5. Consider the Ultimatum Game, as we discussed in class. Assume that instead of being given 100 dollars, I'm given only two dollars. I can offer Chris either 0, 1, or 2 dollars. Chris can either refuse or accept. If he accepts, he gets what I offered him, and I get what's left over. If neither of us accept, neither of us get any money. Construct a payoff matrix for this game. Is there a Nash equilibrium for this game? In your response, be sure to state what a Nash equilibrium is.



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