MAT199 · Erich Prisner · Franklin College · Fall 2008

Test 1

Consider the following two-player game with players Ann and Beth, where Ann has three choices, A1, A2, or A3, and Beth has even four choices, B1, B2, B3, and B4.
  B1    B2    B3    B4  
A1  2,2    3,2    3,3    2,3  
A2  4,1    3,4    5,2    4,1  
A3  1,1    2,3    4,2    3,2  

  1. (1 point) What is the payoff for Beth if Ann plays A2 and Beth plays B3?
  2. (1 point) Find the Maximin moves for both Ann and for Beth.
  3. (1 point) Which moves are strictly dominated by which moves?
  4. (1 point) Which moves are weakly dominated by which moves?
  5. (1 point) Draw the best response digraph.
  6. (1 point) Are there any Nash equilibria?
  7. (1 point) Which move do you think Ann will play? Which move do you think Beth will play? Give a reason.
  8. (1 point) The last question refers to the following zero-sum game:
      L     R  
    U  2    1  
    D  3     4  
    What is Beth's best response to Ann's move "U"? What is Beth's best response to Ann's move "D"?