Payoff Matrix
Problem #4 (page 363)
Consider a game with two players who cannot communicate, and in which each player is asked a question. The players can answer the question honestly or lie. If both answer honestly each receives $100. If one player answers honestly and the other lies, the liar receives $500 and the honest player gets nothing. If both lie, then each receives $50. a) Construct the payoff matrix Honest Player 1 Lie
$100
$100
$500
$0
$500
$0
$50
$50
$100
$100
$500
$0
$500
$0
$50
$50
Honest
P2
Lie
b) What choice will each make? Is there a dominant strategy for either player, is who what is the strategy?
Each will tell the truth. Use the following for questions #14 and #15 (page 365)
Bud and Wise are the only two producers of aniseed beer, a New Age product designed to displace root beer. Bud and Wise are trying to figure out how much of this new beer to produce. They know:
(i) If they both limit production to 10,000 gallons a day, they will make the maximum attainable joint profit of $200,000 a day --- $100,000 a day each.
(ii) If each firm produces 20,000 gallons a day while the other produces 10,000 a day, the one that produces 20,000 gallons will make an economic profit of $150,000 and the other will incur an economic loss of $50,000.
(iii) If both increase production to 20,000 gallons a day, each firm will make zero economic profit. #14 Construct a payoff matrix for the game that Bud and Wise must play
Limit to $10,000 BUD 20,000
Limit to
$100,000
$100,000
$150,000
$50,000
$150,000
$50,000 zero zero
$100,000
$100,000
$150,000
$50,000
$150,000
$50,000 zero zero
10,000
WISE
20,000
#15 Find the Nash equilibrium of the game that Bud and Wise play, does Bud have a dominant strategy, is so what is the strategy?, Does Wise have a dominant strategy, if so what is the strategy?
Nash equilibrium is $100,000. Each will Limit to 10,000
Consider a game with two players who cannot communicate, and in which each player is asked a question. The players can answer the question honestly or lie. If both answer honestly each receives $100. If one player answers honestly and the other lies, the liar receives $500 and the honest player gets nothing. If both lie, then each receives $50. a) Construct the payoff matrix Honest Player 1 Lie
$100
$100
$500
$0
$500
$0
$50
$50
$100
$100
$500
$0
$500
$0
$50
$50
Honest
P2
Lie
b) What choice will each make? Is there a dominant strategy for either player, is who what is the strategy?
Each will tell the truth. Use the following for questions #14 and #15 (page 365)
Bud and Wise are the only two producers of aniseed beer, a New Age product designed to displace root beer. Bud and Wise are trying to figure out how much of this new beer to produce. They know:
(i) If they both limit production to 10,000 gallons a day, they will make the maximum attainable joint profit of $200,000 a day --- $100,000 a day each.
(ii) If each firm produces 20,000 gallons a day while the other produces 10,000 a day, the one that produces 20,000 gallons will make an economic profit of $150,000 and the other will incur an economic loss of $50,000.
(iii) If both increase production to 20,000 gallons a day, each firm will make zero economic profit. #14 Construct a payoff matrix for the game that Bud and Wise must play
Limit to $10,000 BUD 20,000
Limit to
$100,000
$100,000
$150,000
$50,000
$150,000
$50,000 zero zero
$100,000
$100,000
$150,000
$50,000
$150,000
$50,000 zero zero
10,000
WISE
20,000
#15 Find the Nash equilibrium of the game that Bud and Wise play, does Bud have a dominant strategy, is so what is the strategy?, Does Wise have a dominant strategy, if so what is the strategy?
Nash equilibrium is $100,000. Each will Limit to 10,000