Nash equilibrium in the terrorism game

POLI 172

Homework 4                             April 21, 2021

You can work on this homework with 1-4 other classmates (groups of 2-5 total). However, each person must turn in their own assignment. Assignments must be turned in by 4:30 pm on April, 28th (right before class). Late assignments will receive no credit. You may email me to ask for clarification on any question. Or, you can come to office hours next week on Monday.

You should turn in an electronic copy of your homework by uploading it through the course website. You should show your work and explain your answers. Your answers should be neat, and easy to follow.

Like past homeworks this homework is out of 100 points. However, on this homework, you start with 50 points and the questions themselves are worth 55 points on top of that (meaning there is actually an opportunity to get 105/100 points).

Problem 1: Nash equilibrium in the terrorism game

We’ve talked about versions of the game below in class.

Government

Man       Woman

10,−10	50,−50
50,−50	10,−10

Man

Terrorists

Woman

In most of the games we’ve talked about in class, there are Nash equilibria where each player takes a particular action “with certainty,” meaning they take a definite action; they don’t randomly choose each action a certain percent of the time. For example, in the Split or steal game, there is a Nash equilibrium where both players choose steal.

Explain why, in the game above, there is no Nash equilibrium where both players choose a particular action with certainty. For example, there is no Nash equilibrium where the Government chooses Man with certainty and Terrorists play Woman with certainty. (15

points)

Problem 2: Learning in the terrorism game.

Still considering the game above, let’s say that the government plays a sub-optimal strategy. Instead of choosing Man with probability 1/2 and Woman with probability 1/2, the government chooses Man with probability 9/10 and Woman with probability 1/10. Furthermore, assume that the terrorists do choose Man with probability 1/2 and Woman with Probability 1/2.

1. Should the terrorists change their strategy in light of the government’s? (10 points)

1

POLI 172

Homework 4                             April 21, 2021

• Yes, the terrorists would do better if they played Woman more often than 1/2 the time.
• Yes, the terrorists would do better if they played Woman less often than 1/2 the time.
• No, the terrorists cannot improve their payoff by playing Woman more or less often than 1/2 the time.

Problem 3: Signaling theory

Let’s say that you’re considering hanging out with a friend. Your friend just got vaccinated yesterday against Covid-19. So, they haven’t built up any immunity to the virus just yet. Nonetheless, you might still be willing to hang out with this person compared to a person who hadn’t been vaccinated and didn’t know whether or when they intended to get vaccinated. Why or why not?

In writing your answer, think of getting vaccinated as a potential signal of how generally cautious people are about Covid-19. In signaling theory, there have to be

1. Different types of people
2. Different types have to have (or perceive) different costs or benefits to sending the signal, such that some types are willing to send the signal while others are not.

Do you think these requirements apply to the act of getting vaccinated for Covid-19, why or why not? (15 points)

Problem 4: Strategic complements vs substitutes

For one of our game labs, we played a traffic game where players could either take Bellevue or Lake Rd to UCM. Bellevue was quicker all else equal, but both roads became slower as more people used them. In this game, were the strategies (Bellevue or Lake) strategic complements or substitutes? Why? (15 points)

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