Summary: CS 6100 Homework 2
This assignment can be done in groups of one, two or three.
1. In the following strategic-form game, what strategies survive iterated elimination of strictly-dominated
strategies? What are the pure-strategy Nash equilibria?
L C R
T 2,0 1,1 4,2
M 3,4 1,2 2,3
B 1,3 0,2 3,0
2. Agents 1 and 2 are bargaining over how to split a dollar. Each agent simultaneously names shares they would
like to have (s1 and s2) where 0 s1 1 and 0 s2 1. If s1+s2 1 then both agents receive the shares they
named; if s1+s2 >1, then both agents receive zero. Draw the best response function for both players (if player 1
picks x, should you player y do if he knew). What are the pure strategy equilibrium of this game? Hint, to
make it easier, consider a fixed set of choices, say 0, .2, .4, .6, .8, 1 for each player.
Hint: A best response function says, "If player A does x, what is player B's response (shown on y axis)." And
conversely, if player B does y, what is player A's response (shown on x axis). It works out nicely if you can
draw both functions on the same set of axis. The point where they cross is equilibrium.
3. At a fishing booth at a carnival, two children randomly get prizes. There are 5 types of prizes of varying
values. Assume, a prize of type 5 is the best and a prize of type 1 is the worst. They both get a prize that they
don't show to other. All prizes occur with the same frequency, so they don't assume there are more of the bad
prizes. They are both asked if they want to exchange the prizes they were given. If both want to exchange, the