Exam 28: A: Game Applications

(See Problem 3.) 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 48 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

Suppose that in the Hawk-Dove game discussed in Problem 8, the payoff to each player is -9 if both play Hawk. If both play Dove, the payoff to each player is 5, and if one plays Hawk and the other plays Dove, the one that plays Hawk gets a payoff of 9 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

Suppose that in the Hawk-Dove game discussed in Problem 8, the payoff to each player is -8 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 a. .19. b. .69. c. .38. d. .10. e. 1

(See Problem 6.) Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the Trough. If both pigs choose Wait, both get 3. If both pigs Press the Button, then Big Pig gets 9 and Little Pig gets 1. 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, then Big Pig gets 7 and Little Pig gets 4. In Nash equilibrium,

(See Problem 6.) Big Pig and Little Pig have two possible strategies, Press the Button, and Wait at the Trough. If both pigs choose Wait, both get 4. If both pigs Press the Button, then Big Pig gets 7 and Little Pig gets 3. 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, then Big Pig gets 2 and Little Pig gets 5. In Nash equilibrium,