GraduateGameTheoryHomework3-Answers - Homework Assignment#3...

Homework Assignment #3
Graduate Game Theory
1. Iterated Deletion of Dominated Strategies. Consider the following 3 player game. Each
player i ∈ { 1 , 2 , 3 } simultaneously names a real number a
i
∈ [0 , 100]. Then the set of
winners are the players whose choices are closest to p
∑
3
i =1
a
i
. The value of not winning
is normalized to equal 0. Letting the number of winners from a profile of choices a =
( a
1
, a
2
, a
3
) be denoted by w ( a ), the payoff from winning is equal to w ( a )
- 1
.
(a) Suppose that 0 < p < 1. What are the dominated strategies? (Hint: it will be
a function of p . It can help to set some value of p ∈ (0 , 1) and derive the set of
dominated strategies for that given value of p as a first step.)