Fictitious Play Homework

The purpose of this homework is to have you learn fictitious play.

Program up the ficitious play algorithm to do the following.

  1. Battle of the sexes.
    1. What solution occurs if initial weights are set as  Kman(Cooperate)=Kwoman(Defect)=1, and Kwoman(Cooperate)=Kman(Defect)=0? 
    2. What solution occurs if initial weights are set as  Kman(Cooperate)=Kwoman(Defect)=0, and Kwoman(Cooperate)=Kman(Defect)=1?
  2. The coordination game
    3. Row/Column
    C
    D
    C
    (2,2)
    (0,0)
    D
    (0,0)
    (1,1)
    1. What solution is chosen?
    2. Does the solution depend on initial weights?
  3. Matching pennies
    4. Row/Column
    Heads
    Tails
    Heads
    (1,-1)
    (-1,1)
    Tails
    (-1,1)
    (1,-1)
    1. What do the phase trajectories look like when initial weights are K(Heads)=K(Tails)=1?  Use these initial weights for both players.
    2. What do the phase trajectories look like when initial weights are K(Heads)=1000 and K(Tails)=1?  Use these initial weights for both players.
    3. What solution is chosen for each of the initial conditions?
  4. Shapley's game
    5. Row/Column L M R
    T (0,0) (1,0) (0,1)
    M (0,1) (0,0) (1,0)
    D (1,0) (0,1) (0,0)
    1. Does this game converge? Justify your answer.
    2. What do the phase trajectories look like?
Since I won't look at your code, make sure that your discussion justifies your answers.  Pretend that you are writing an essay on an exam and that you must convince me that not only can you generate an answer but also that your answer is right.