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
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