Unformatted text preview: Problem
1.
Consider a game in the normal form:
Player 1
Player
2 T
B L
3, 4
2,3 R
2,1
5,4 a) Find NE in a simultaneous game.
b) Hereafter assume that player 1 moves first (L or R), after that player 2 moves (T or B). Draw
the tree of the sequential game
c) Find SPNE. Problem 2.
Consider the following payoff matrix:
Player
1
T
B
Player
2
L
R
3,x
2,2
2,3
y,5
Under what conditions on x and y is there a dominant strategy equilibrium? That is, find all possible
dominant strategy equilibria to this game for all pairs of x and y. Problem 3.
Consider the following payoff matrix 1. Find the pure strategy Nash equilibria of the simultaneous game
2. Now suppose the game is played sequentially. Find the subgame perfect equilibrium if player 1 goes
first and if player 2 goes first.
3. Discuss whether each of the players would want to go first or second. Solution to problem 1.
a) NE:
1) {L,T} 2) {B,R}
Player 1
Player
2 L
3, 4
2,3 T
B R
2,1
5,4 b) The tree of the game:
Player 1
L
R
Player 2
T
B
T
B
(4,3)
(3,2)
(1,2)
(4,5)
Outcome={player 1’s utility, player 2’s utility } c) SPNE
1) {Player 1: L; Player 2: TL and BR}
2) {Player 1: R; Player 2: BR and TL } Solution to problem 2.
If x < 2, then R is a dominating strategy for player 2. If also y < 2, then T is also a dominating
strategy for player 1. This results in a dominating equilibrium (T,R). For any other choice of x and
y, no dominating strategies exist for both players, i.e. no other dominating equilibria can be found. Solution to problem 3.
1. Two NE: (C;R) and (B;R)
2. If Player 1 moves first, SPNE is (B; LT, RC, MB)
If Player 2 moves first, SPNE is (BL, BM, CR; R)
3. Each player would want to go first. ...
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 Fall '08
 Buddin
 Game Theory, player

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