Exam 15: Game Theory: the Mathematics of Competition

In the following game of batter-versus-pitcher in baseball, the batter's batting averages are shown in the game matrix. What is the pitcher's optimal strategy?

In a truel where the choices are simultaneous, what is the probability that any particular player will survive?

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. Does this game have a saddlepoint? What is each player's minimax or maximin strategy? Justify your response.

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. Which of the following statements is true?

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. Does this game have a saddlepoint? What is each player's minimax or maximin strategy? $\left[ \begin{array} { l l } 5 & 7 \\4 & 3\end{array} \right]$

Use the following information to answer the Questions: -Which of the following is a Nash equilibrium?

Use the following information to answer the Questions: In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. $\left[ \begin{array} { c c c c } - 3 & 4 & 1 & 2 \\6 & - 1 & 2 & 1 \\3 & 2 & 3 & 6 \\1 & - 4 & 2 & 5\end{array} \right]$ -The maximin strategy of player I is:

If you cheat on your income tax return you will pay $1000 in taxes; if you don't cheat you will pay $2000. If you are audited and you didn't cheat, your auditor will be kind and reduce your taxes from $2000 to $1500. If you are audited and you did cheat, you will be caught and have to pay a total of $2500, including penalties. Assuming the government wants to receive as much money as possible, statistically, which is the best option for the government to choose?

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. The minimax strategy of player II is:

In the following game of batter-versus-pitcher in baseball, the batter's batting averages are shown in the game matrix. What is the batter's optimal strategy?

A mixed strategy assigns some probability for each pure strategy such that the specific strategy used in any given play of the game can be selected using some appropriate randomization device.

Suppose on a committee of three people Kim (the chair), Chris, and Terry each have one vote, but Kim breaks any tie. In attempting to elect someone to host the summer picnic, each person has a priority list: \mid Kim's Priorities Chris's Priorities Terry's Priorities 1st choice \mid Kim Chris Terry 2nd choice \mid Terry Kim Chris 3rd choice \mid Chris Terry Kim Which of the following are Nash equilibria? I: Every person votes for Kim. II: Every person votes for Chris.

Describe a payoff matrix of a two-person total-conflict game.