Comparative HW 3

Stag Hunt Game: The story of the stag hunt is that two hunters are hunting a deer in the forest. It requires the cooperation of both hunters to capture the deer, which can feed the entire village. Instead of cooperating, though, the hunters can choose to defect to capture a rabbit, which will feed only their own family. Hunters prefer to cooperate and capture the deer, but do not want to be left waiting for their comrade if he or she runs off to get a rabbit. The preference ordering for player 1 is the following: CC>DC>DD>CD. The preference ordering for player 2 is the following: CC>CD>DD>DC. C = cooperate (deer), D = defect (rabbit). We list player 1's action first, then player 2's action, i.e. CD means player 1 chooses C and player 2 chooses D. Using the ordinal payoffs (4, 3, 2, 1), fill in the payoff matrix in Game 7 on the pdf. What is the Nash equilibrium or equilibria for the game?

(C; C) (D;D)

Game of Chicken or the game from the film Footlose: I am one of two drivers racing down a deserted road, and you are the other. We are racing straight at each other. Our friends are watching us to see who has more guts. I want you to swerve while I keep going. If you swerve, you are a chicken and I gain status among our peers. If both of us swerve, then its an OK outcome because neither of us gains or loses respect, and we both may gain some respect with everyone else just because we played. If I swerve and you don't, then I am chicken and lose status among our peers; I don't like this much. But if neither swerves, we are both dead and it doesn't matter - this is the worst possible outcome. The preference ordering for player 1 is the following: DC>CC>CD>DD. The preference ordering for player 2 is the following: CD>CC>DC>DD. C = cooperate (Swerve) and D = defect (drive straight). Using the ordinal payoffs (4, 3, 2, 1), fill in the matrix in Game 8 on the pdf. What is the Nash equilibrium or equilibria for this game?

(C; D) (D; C)

What is the Nash equilibrium or equilibria in Game 1 on the pdf

(D; d)

Free trade occurs when goods and services between countries flow unhindered by government-imposed restrictions such as tariffs, quotas, and anti-dumping laws that are often designed to protect domestic industries. Although it is well-known that free trade creates winners and losers, a broad consensus exists among most economists that free trade has a large and unambiguous net gain for society as a whole. For example, Robert Whaples (2006) finds in a survey of economists that "87.5% agree that the U.S. should eliminate remaining tariffs and other barriers to trade" and that "90.1% disagree with the suggestion that the U.S. should restrict employers from outsourcing work to foreign countries." Despite this consensus, it is not at all clear that countries will actually adopt policies promoting free trade. Consider the following strategic situation in which the US and the EU are engaged in trade negotiations. Both countries must decide whether to reduce their tariffs or impose new tariffs. The best outcome for both countries is for them to impose new tariffs and for the other side to reduce tariffs; they can export more easily to the other country and they obtain increased revenue from the new tariffs. The worst outcome for both countries is for them to reduce tariffs and for the other country to increase tariffs; they will lose jobs due to reduced exports and the other country will benefit from their lower tariffs. Of the remaining two outcomes, both countries prefer the outcome where they reduce tariffs to the one where they both impose new tariffs. If both countries reduce their tariffs, then each country can benefit from increased free trade. If both countries impose new tariffs, there is a trade war in which each country sees a decline in trade and a loss of jobs. Based on this story, the preference-ordering for the EU over the four possible outcomes is:· Impose; Reduce > Reduce; Reduce > Impose; Impose > Reduce; Impose and the preference-ordering for the U.S. is: · Reduce; Impose > Reduce; Reduce > Impose; Impose > Impose; Reduce, where the EU's action is given first, the U.S.'s action is given second, and ">" means "is strictly preferred to". Using the ordinal preferences (4, 3, 2, 1) to capture these preference orderings, fill in the empty payoff matrix in Game 6 on the pdf. What is (are) the Nash equilibrium (equilibria) of the game?

(Impose Tariffs; Impose Tariffs)

What is (are) the Nash equilibrium (equilibria) in the game?

(Switch to Blu-Ray, Blu-Ray) and (HD DVD; Switch to HD DVD)

What is the Nash equilibrium or equilibria of Game 4 on the pdf?

(U; d)

What is the Nash equilibrium or equilibria in Game 2 on the pdf?

(U; u) (D; d)

What is the Nash equilibrium or equilibria of Game 3 on the pdf?

(U; u) (D; d)

In an American football game, we can think that the offense has four possible strategies to progress down the field: run the ball, short throws, medium throws, and long throws. The defense has three strategies to try to stop this: counter the run, counter the pass, or blitz the quarterback. Let's say that after studying many games, statisticians have come up with the payoff matrix shown in Game 9 on the pdf, where the numbers in each cell indicate the expected number of yards either gained by the offense or lost by the defense. As you can see, every yard gained by the offense is a yard lost by the defense. As always, the players prefer higher numbers to lower numbers. What is (are) the Nash equilibrium (equilibria)?

(short pass; counter pass)

In 2006, there were a number of media reports about the next generation of DVD players which produce picture and sound that is much clearer than that produced by current machines. However, there are two competing formats, Blu-ray (Sony) and HD DVD (Toshiba). Both are affiliated with certain movie studios, who have agreed to release their movies in one or the other of the new formats. This creates a problem for the producers of this new technology - each wants their own version to win out, but by competing they make it entirely likely that most consumers will sit back and wait until there is (a) a clear winner or (b) a newer, even better, method of supplying movies is developed by someone else. If this happens, both Sony and Toshiba lose out.Imagine that both companies have developed a new product, but with different formats. If one of the companies would be willing to switch quickly (assume that copyright laws would allow them to produce something similar), that company would lose some time and market share, but be able to get into the market. Consumers would be more willing to buy the new technology, and both companies would make more money. If neither company is willing to coordinate with the other, they end up in a war of attrition, with fewer customers. This is shown in Game 5 on the pdf. What payoff would Toshiba get if it chose to produce HD DVD, while Sony chose to produce Blu-Ray?

2

What payoff would Sony get if it chose to switch to HD DVD while Toshiba chose to produce HD DVD?

3

Which of the following preference orderings describes the way that Toshiba ranks the four possible outcomes? (Note: if X > Y, then X is preferred to Y.)

Both players produce HD DVD > Both players produce Blu-Ray > Toshiba produces HD DVD, Sony produces Blu-Ray > Toshiba produces Blu-Ray, Sony produces HD DVD

Which players have a dominant strategy and what are they in Game 3 on the pdf?

Neither player has a dominant strategy

Which players have dominant strategies and what are they in Game 2 on the pdf?

Neither player has a dominant strategy

Does the defense have a dominant strategy in the American Football Game?

No

Does the offense have a dominant strategy in the American Football Game?

No

Which players have dominant strategies in Game 1 on the pdf and what are they?

Player 1 has a dominant strategy (D) and Player 2 has a dominant strategy (d)

Which players have a dominant strategy and what are they in Game 4 on the pdf?

Player 1 has a dominant strategy (U)

What is (are) the expected outcome (outcomes) of the game?

Since there was more than one Nash equilibrium, it is difficult to say what the actual outcome of the game will be

In the game, do the players (Sony and Toshiba) move simultaneously or sequentially?

simultaneously

What is (are) the expected outcome (outcomes) of the Free Trade game?

trade war

Does the EU have a dominant strategy in the Free Trade Game

yes, impose new tariffs

Does the US have a dominant strategy in the Free Trade Game

yes, impose new tariffs