Game Theory Assignment, Part 2 It may be easiest to work out the problems by hand (drawing trees and such), scan it, and then send me the scanned copied. However you choose to do it, please send me...

Game Theory Assignment, Part 2

It may be easiest to work out the problems by hand (drawing trees and such), scan it, and then send me the scanned copied. However you choose to do it, please send me ONE file with your answers. Please do not send multiple files (e.g. one for a tree, one for text, one for tables, etc.). You will submit this assignment as one attachment using the Assignments tool.

Problem 1

In each of the games shown below, players 1 and 2 must move at the same time without knowledge of the other player's move. The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2). Using game theoretic logic, determine the Nash equilibrium for each game.
a. If either player has a dominant strategy, circle what it is (i.e. circle up or down, left or right). Do not circle an action if is not a dominant strategy.
b. Circle the predicted outcome(s) to the game (i.e. circle (4, 3) or (6, 2) or (3, 1) or (4, 0)

2 points	Player 2
Player 1	Left	Right
Up	4, 3	7, 2
Down	3, 1	4, 4

2 points	Player 2
Player 1	Left	Middle	Right
Up	3, 4	3, 6	4, 5
Middle	10, 5	2, 7	3, 6
Down	5, 4	2, 6	3, 4

2 points	Player 2
Player 1	E	F	G	H
A	5, 7	4, 4	7, 6	10, 5
B	0, 7	5, 8	8, 9	16, 5
C	3, 5	4, 3	5, 4	18, 3
D	0, 10	2, 13	0, 15	8, 8

Problem 2

Consider the following three person color game between Hillary, Laura, and Michelle. Each player can choose either Red or Blue. The payoffs for these choices are shown below. The first payoff in each cell is for Hillary, the second payoff is for Laura, and the third payoff is for Michelle.

Michelle Red
Laura Red	Laura Blue
Hillary Red	6, 6, 6	1, 10, 1
Hillary Blue	10, 1, 1	2, 2, 1

Michelle Blue
Laura Red	Laura Blue
Hillary Red	1, 1, 10	1, 2, 2
Hillary Blue	2, 1, 2	2, 2, 2

1. Assume this game is only played one time. What outcome would game theory predict? Why? (3 points)

1. What advice would you give the players on how to play this game? (1 point)

Problem 3

Imagine that there are two snowboard manufacturers (FatSki and WideBoard) in the Reno market. Each firm can either produce 10 or 20 snowboards per day. The table below shows the profit per snowboard for each firm that will result given the joint production decisions of these two firms.

Number of Snowboards Produced by:	Total Industry Production Per Day	$ Profit Per Snowboard
FatSki	WideBoard
10	10	20	240
10	20	30	180
20	10	30	180
20	20	40	96

1. Draw the game payoff matrix for this situation. (2 points)

1. Does either player have a dominant strategy? If so, what is it? (1 points)

1. What is the Nash equilibrium solution and how many boards should each player produce each day? (1 points)

1. Since FatSki and WideBoard must play this game repeatedly (i.e. make production decisions every day), what strategy would you advise them to play in order to maximize their payoff over the long term? (1 point)

Challenge Question


(Up to 7 points Extra Credit)
In the game shown below, players 1 and 2 must move at the same time without knowledge of the other player's move. The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2).
Find the Nash equilibrium(s) for this game. You will need to use a combination of techniques to solve this problem.

Player 2
Player 1	Left	Middle	Right
Up	4, 5	4, 6	10, 1
Middle	6, 4	3, 3	9, 2
Down	2, 10	2, 12	8, 3