Exam 29:Game Theory-Part A

Suppose that in a Hawk-Dove game similar to the one discussed in your workbook,the payoff to each player is -9 if both play Hawk.If both play Dove,the payoff to each player is 4,and if one plays Hawk and the other plays Dove,the one that plays Hawk gets a payoff of 5 and the one that plays Dove gets 0.In equilibrium,we would expect hawks and doves to do equally well.This happens when the proportion of the total population that plays Hawk is

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?

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 3.If both pigs choose Press the Button,then Big Pig gets 8 and Little Pig gets 2.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 2 and Little Pig gets 1.In Nash equilibrium,

Suppose that in a Hawk-Dove game similar to the one discussed in your workbook,the payoff to each player is -6 if both play Hawk.If both play Dove,the payoff to each player is 4,and if one plays Hawk and the other plays Dove,the one that plays Hawk gets a payoff of 6 and the one that plays Dove gets 0.In equilibrium,we would expect hawks and doves to do equally well.This happens when the proportion of the total population that plays Hawk is

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

In the town of Torrelodones,each of the N $\gt$ 2 inhabitants has $100.They are told that they can all voluntarily contribute to a fund that will be evenly divided among all residents.If $F are contributed to the fund,the local K-Mart will match the private contributions so that the total amount to be divided is $2F.That is,each resident will get back a payment of $2F/N when the fund is divided.If the people in town care only about their own net incomes,in Nash equilibrium,how much will each person contribute to the fund?

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

The coach of the offensive football team has two options on the next play.He can run the ball or he can pass.His rival can defend either against the run or against the pass.Suppose that the offense passes.Then if the defense defends against the pass,the offense will make zero yards,and if the defense defends against the run,the offense will make 25 yards.Suppose that the offense runs.If the defense defends against the pass,the offense will make 10 yards,and if the defense defends against a run,the offense will gain 2 yards. a.Write down a payoff matrix for this game. b.Is there a Nash equilibrium in pure strategies for this game? If so,what is it? If not,demonstrate that there is none.

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

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?

Suppose that in a Hawk-Dove game similar to the one discussed in your workbook,the payoff to each player is -6 if both play Hawk.If both play Dove,the payoff to each player is 3,and if one plays Hawk and the other plays Dove,the one that plays Hawk gets a payoff of 8 and the one that plays Dove gets 0.In equilibrium,we would expect hawks and doves to do equally well.This happens when the proportion of the total population that plays Hawk is

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 432 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.

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 63 + 0.30X.What is a long-run equilibrium attendance for this club?

George and Sam have taken their fathers' cars out on a lonely road and are engaged in a game of Chicken.George has his father's Mercedes and Sam has his father's rattly little Yugoslavian-built subcompact car.Each of the players can choose either to Swerve or to Not Swerve.If both choose Swerve,both get a payoff of zero.If one chooses Swerve and the other chooses Not Swerve,the one who chooses Not Swerve gets a payoff of 10 and the one who chooses Swerve gets zero.If both choose Not Swerve,the damage to George's car is fairly minor and he gets a payoff of -5,while for Sam the results are disastrous and he gets a payoff of-100.

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.

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

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

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 Big Pig gets 5 and Little Pig gets 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 6 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?