Exam 5: Game Theory

Return to the version of the game between the fishermen in which they fish independently. If the marginal cost for just fisherman A went up,what would be the likely effect on the Nash equilibrium?

When a game has multiple equilibria,a useful method to sort out which one would be the "best" prediction is to

Two games that differ only in the timing of moves-one simultaneous,the other sequential move-can sometimes have completely different subgame-perfect equilibria. Why?

In what way or ways can strategies more complicated than simple actions?

Best-response functions

A lake supports a delicious variety of fish. The land around the lake is owned by two fisherman,so by state law both are free to fish as much as they like. Let FA and FB be the number of fish each catches,respectively. Suppose the price of fish is 100 - FA - FB. Given this demand curve,it turns out that marginal revenue is 100 - 2FA - FB for fisherman A and 100 - FA - 2FB for fisherman B. What is the total number of fish by both in the Nash equilibrium?

If the Prisoners' Dilemma is repeated over and over again with the same two players having an indefinite time horizon,

A football team has the chance of scoring the game-winning touchdown on the last play of the game. It can either run or pass. The defense can play for the run or play for the pass.The following normal form lists the payoffs from the game made up by this last play. The payoffs are probabilities of winning the game. What is the defense's dominant strategy?

A football team has the chance of scoring the game-winning touchdown on the last play of the game. It can either run or pass. The defense can play for the run or play for the pass. The following normal form lists the payoffs from the game made up by this last play. The payoffs are probabilities of winning the game. The Nash equilibrium is (equilibria are)

Consider the same game between the fishermen in the previous question. How does the total number of fish caught in the Nash equilibrium compare to the number they would catch if they belonged to same company,so shared revenues and costs equally?

Consider the same football situation as in the previous question,but now suppose the probabilities of winning are less extreme than before,given by the following normal form: What is the defense's dominant strategy?

Teens A and B are smitten with each other but neither knows of the other's feelings.Suppose the teachers at their school organize a dance.The "payoff" is based on whether their advances are rebuffed or accepted.If they both Declare, they get positive utility but if they are Rebuffed they face humiliation (significantly negative payoff). Rebuffing an advance slightly elevates the teen's standing with peers. ?? What is a teen's dominant strategy?

Consider the same football setting as in the previous question,but now suppose the payoffs (probabilities of winning)are given by the following normal form: ? The Nash equilibrium is (equilibria are)

Consider the game between the teens from the previous question. In addition to any pure-strategy Nash equilibrium,there is another one in mixed strategies. In it,each teen chooses to declare with probability

The Prisoners' Dilemma is so named because

Consider the game between the teens from the previous question.The pure-strategy Nash equilibrium is (equilibria are)

Consider the same football situation as in the previous question,but now suppose the payoffs (probabilities of winning)are as given in the following normal form: Which team has a dominant strategy?

The game of Matching Pennies

A teacher curves the final exam such that the top half of students get an A and the bottom half an F (so their grade depends only on relative and not absolute performance). Suppose that there are equal numbers of two groups,the Brainiacs and the Numbskulls. If they both study or they both party,the Brainiacs will get the As but if the Brainiacs party and the Numbskulls study,the Numbskulls will get the As.Suppose further that they both dislike studying and both like good grades. Suppose all students of a type choose the same action (so we can view it as a two-player game). The payoff matrix is ? Characterize the Nash equilibrium or equilibria:

Consider the game between the teens from the previous question. Instead of being a simultaneous game,suppose it is sequential,with teen A moving first. What is the subgame-perfect equilibrium of this new game?