Microeconomics Chapter 13 Homework
Identify the key assumption(s) made about a Nash equilibrium.
All players understand the game and the payoffs associated with each strategy. All players understand that other players understand the game.
Is a player's best response in a game the same as his dominant strategy?
Not necessarily. If a player has a dominant strategy, then it is his best response; however, every best response is not always a dominant strategy.
What must you, as the consultant, construct for Chevron before you can determine if there is a dominant strategy equilibrium?
Payoff matrix.
What is the Nash equilibrium?
The Nash equilibria are for Station A to pick C and Station B to pick R and for Station A to pick R and Station B to pick C.
What is backward induction?
The procedure of solving an extensive-form game by first considering the last mover's decision.
The game is played between two players, Player A and Player B. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), Player A keeps both pennies. If the pennies do not match (one heads and one tails), Player B keeps both pennies. Construct the payoff matrix for Player A and Player B. Player A _____________ a dominant strategy, and Player B ___________ a dominant strategy.
(+1/-1),(-1/+1) (-1/+1),(+1/-1) does not have, does not have, example of a zero-sum game, no nash equilibrium
Imagine a game in which two drivers drive toward each other on a collision course: one must swerve, or both may die in the crash, but if one driver swerves and the other does not, the one who swerved will be called a "chicken," meaning he is a coward. If they both go straight, then they both die, earning dash-10 happiness points each. If one goes straight and the other swerves, then the brave driver gets 5 points of happiness and the "chicken" loses 2 points of happiness. If both drivers swerve, then it is a tie and nobody earns any happiness points. Construct the payoff matrix for Driver 1 and Driver 2.
(-10,-10) (5,-2) (-2,5) (0,0)
Use a matrix to model a two-player game of rock-paper-scissors with a payoff of 1 if you win, dash-1 if you lose, and 0 if you tie. Why should you use a mixed strategy to play this game?
(0/0),(-1,1),(1/-1) (1/-1),(0,0),(-1,1) (-1,1),(1,-1),(0,0) There is no Nash equilibrium. Predictable behavior by one player can be taken advantage of by the other player.
Two gas stations, A and B, are locked in a price war. Each player has the option of raising its price (R) or continuing to charge the low price (C). They will choose strategies simultaneously. If both choose C, they will both suffer a loss of $negative 25−25. If one chooses R and the other chooses C, (i) the one that chooses R loses many of its customers and earns $00, and (ii) the one that chooses C wins many new customers and earns $250250. If they both choose R the price war ends and they each earn $125125. Does either player have a dominant strategy? Explain.
The stations do not have dominant strategies because what works best depends on what the other station does.
What elements must be known to set up a simultaneous move game?
The players, the strategies, the payoffs.
The United States's best response when Russia chooses to not invade is _________. The United State's best response when Russia chooses to invade is _________. Russia's best response when the United States chooses to be tough is __________. Russia's best response when the United States chooses to make concessions is _______. The Nash equilibrium is ____________.
Tough, Tough, Not Invade, Invade Tough/Not Invade
Why might game theory not always be an accurate predictor of real-world situations?
We do not always know the exact payoffs, since payoffs involve attitudes and feelings as well as monetary gains.
Two firms are thinking of entering a new market. If one enters it will be successful but if a second enters both will suffer very large losses. Is there a first-mover advantage in this game?
Yes. The firm that goes first can enter and the firm that goes second will have no incentive to enter.
A pure strategy involves ____________. Suppose that a goalie is playing a mixed strategy between diving to the left and the right. A player decides which strategy to employ when playing a game with mixed strategies by choosing ____________.
choosing one particular action for a situation. randomly.
Driver 1 ________ a dominant strategy, and Driver 2 _____________ a dominant strategy. Nash Equilibruim?
does not have, does not have Box 2 and 3
After you examine the payoffs, you discern that BP's best response is to always bid low. Then bidding low would be BP's _____________.
dominant strategy
If Bill acts as a secure monopoly and produces a low quantity at a high price, then Larry will ________. If Bill acts as an insecure monopoly and produces a greater quantity at a lower price, then Larry will _________. The logical move for Bill is to produce a ____________. Assuming Bill acts logically, then the logical move for Larry is to ________. Assuming Bill and Larry act logically, then Bill's profit will be _________ and Larry's profit will be ______. This is an example of: ____________
enter, stay out, high quality, stay out $10,000, $0 an extensive game
When can backward induction be used to arrive at the equilibrium for a game? In the case of,
extensive form games.
Based on this __________, the people ___________ this politician. Suppose that a new idealistic political party publicly promises before the election that if the politician sells out after he is elected, then it would use its considerable power and influence to impeach the politician and throw him in prison. If this threat is credible, then the people __________ elect the politician because the _________ of the new political party changes the payoff the politician faces.
extensive-form game, should not elect, should , commitment
What is not an example of a real life zero sum game?
free market transaction.
A first-mover advantage occurs if __________. Suppose you were playing rock-paper-scissors as an extensive from game; first you choose rock, or paper, or scissors, and then your opponent makes a choice. Is there a first-mover advantage in this game?
the first mover to act in a sequential game gets a benefit from doing so. No, if you show your move first you will lose every time.
A zero-sum game is when ___________.
the sum of the payoffs is zero.
A Nash equilibrium is ___________.
when players choose strategies that are best responses to the strategy of others.
Suppose that a player has a dominant strategy. Would she choose to play a mixed strategy (such as playing two strategies each with probability 50-50)? Why or why not?
No, because it would involve choosing actions other than the dominant strategy.
In a game with mixed strategies, does either of the players have a dominant strategy? Why or why not?
no, because the best choice in a mixed strategy game is to pick a random strategy.
David's dominant strategy is _________, and Jordan's dominant strategy is _________. The Nash equilibrium is ___________.
Low Price, Low Price, D
Astounding's dominant strategy is __________ and Broadcast's dominant strategy is _____________. The equilibrium is __________.
Medium, No Dominant Strategy, Medium/Medium
How is a Nash equilibrium different from a dominant strategy equilibrium?
For a given game, there can only be one dominant strategy equilibrium but multiple Nash equilibriums.
One of your coworkers, Freddie, really gets on your nerves and it would dramatically increase your happiness if he was fired. Freddie also dislikes you and wishes you would be fired. You have the option of going to your boss and lying about Freddie harassing you, which you are sure will get him fired. Freddie has the same option to make up a lie about you to get you fired. Whoever gets fired will not have any credibility to have his lies believed afterward. Given these circumstances, it would be logical for you to The person who lies first in this situation has a Given these circumstances, it would be logical for you to The person who lies first in this situation
lie first to get Freddie fired first-mover advantage do nothing suffers reputational damage
