Exam 28: Game Applications

Alec and Kim used to be much better friends than they are now. The problem is what to do about Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is Kim Under the circumstances, Alec should publicly announce at Thanksgiving that he is not buying a Christmas gift for Kim.

Consider the goalie's anxiety at the penalty kick. Let the kicker's payoffs below represent the kicker's probability of success and the goalie's payoffs the probability of failure. Goalie The goalie should defend left with probability

Suppose AMD is considering cloning Intel's latest CPU chip. If AMD enters Intel's market, Intel can play Mean, expand its output, drop prices, and try to make AMD's profit as small as possible or play Nice by cutting back its output and sharing the market. AMD and Intel both know that after all moves are complete, the time-discounted profits of future chip production in billions of dollars are Intel Assuming AMD moves first, which of the following is the Nash equilibrium for sequential play?

Recall from the movie Dr. Strangelove, General Turgison (played by George C. Scott) remarks, "Boy, I sure wish we had one of those Doomsday Machines." If both the United States and the Soviet Union possess a Doomsday Machine, the payoffs for a simultaneous attack are as follows: U.S.S.R. Would it be desirable from the U.S. perspective to have its own Doomsday Machine? Explain why or why not?

In a small isolated town, there are two types of people, saints and crooks. In business dealings between any two residents of this town, the payoffs are below. What percentage of this town's residents would be saints in an evolutionary stable strategy?

In the classic 1960s macabre comedy Dr. Strangelove, the Soviet Union constructed a Doomsday Machine which would end all life on earth if ever the Soviet Union were attacked. In the movie, the existence of the Doomsday Machine was kept secret. This would enhance the effectiveness of such a machine.

Alec and Kim used to be much better friends than they are now. The problem is what to do about Christmas gifts? If they wait until Christmas morning and move simultaneously, their payoff matrix is Kim If Alec commits at Thanksgiving time not to buy a gift for Kim, Kim will find it in her best interest

An equilibrium in a sequential game is always a Nash equilibrium in a simultaneous game with equivalent payoffs.