Exam 27: Game Theory-Part A

A game has two players and each has two strategies.The strategies are Be Nice and Be Mean.If both players play Be Nice, both get a payoff of 5.If both players play Be Mean, both get a payoff of 23.If one player plays Be Nice and the other plays Be Mean, the player who played Be Nice gets 0 and the player who played Be Mean gets 10.Playing Be Mean is a dominant strategy for both players.

In the prisoner's dilemma game, if each prisoner believed that the other prisoner would deny the crime, then both would deny the crime.

A game has two players.Each player has two possible strategies.One strategy is Cooperate, the other is Defect.Each player writes on a piece of paper either a C for cooperate or a D for defect.If both players write C, they each get a payoff of $100.If both players write D, they each get a payoff of 0.If one player writes C and the other player writes D, the cooperating player gets a payoff of S and the defecting player gets a payoff of T.To defect will be a dominant strategy for both players if

A two-person game in which each person has access to only two possible strategies will have at most one Nash equilibrium.

A general has the two possible pure strategies, sending all of his troops by land or sending all of his troops by sea.An example of a mixed strategy is where he sends 1/4 of his troops by land and 3/4 of his troops by sea.

If the number of persons who attend the club meeting this week is X, then the number of people who will attend next week is 80 + 0.20X.What is a long-run equilibrium attendance for this club?

Two players are engaged in a game of Chicken.There are two possible strategies, Swerve and Drive Straight.A player who chooses to Swerve is called Chicken and gets a payoff of zero, regardless of what the other player does.A player who chooses to Drive Straight gets a payoff of 32 if the other player swerves and a payoff of -48 if the other player also chooses to Drive Straight.This game has two pure strategy equilibria and

If a game does not have an equilibrium in pure strategies, then it will not have an equilibrium in mixed strategies either.

A situation where everyone is playing a dominant strategy must be a Nash equilibrium.

Professor Binmore has a monopoly in the market for undergraduate game theory textbooks.The time-discounted value of Professor Binmore's future earnings is $2,000.Professor Ditt is considering writing a book to compete with Professor Binmore's book.With two books amicably splitting the market, the time-discounted value of each professor's future earnings would be $200.If there is full information (each professor knows the profits of the other), under what conditions could Professor Binmore deter the entry of Professor Ditt into his market?

If the number of persons who attend the club meeting this week is X, then the number of people who will attend next week is 90 + 0.40X.What is a long-run equilibrium attendance for this club?

Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the Trough.If both pigs choose Wait at the Trough, both get 2.If both pigs choose Press the Button, then both pigs get 5.If Little Pig presses the button and Big Pig waits at the trough, then Big Pig gets 10 and Little Pig gets 0.Finally, if Big Pig presses the button and Little Pig waits at the trough, then Big Pig gets 3 and Little Pig gets 2.In Nash equilibrium,

Professor Binmore has a monopoly in the market for undergraduate game theory textbooks.The time-discounted value of Professor Binmore's future earnings is $4,000.Professor Ditt is considering writing a book to compete with Professor Binmore's book.With two books amicably splitting the market, the time-discounted value of each professor's future earnings would be $400.If there is full information (each professor knows the profits of the other), under what conditions could Professor Binmore deter the entry of Professor Ditt into his market?

Professor Binmore has a monopoly in the market for undergraduate game theory textbooks.The time-discounted value of Professor Binmore's future earnings is $2,000.Professor Ditt is considering writing a book to compete with Professor Binmore's book.With two books amicably splitting the market, the time-discounted value of each professor's future earnings would be $200.If there is full information (each professor knows the profits of the other), under what conditions could Professor Binmore deter the entry of Professor Ditt into his market?