Question

Suppose that 100 million Americans are each given $100 and needs to decide whether to: 1. Buy a pair of jeans, or 2. Contribute $100 to a system protecting earth from collisions with asteroids. (These are the only two options as far as spending these $100.) The probability that an asteroid is deflected is equal to the proportion of these 100 million Americans who decide to give $100 toward asteroid protection suppose that each of the 100 million Americans attaches a value of $1 to an increase of 1% in the chance of asteroid deflection. Also suppose that each each of the 100 million Americans attaches a value of $100 to the pair of jeans they could buy instead of giving to asteroid protection Which of the following statements is true?

a. Buying jeans is a dominant strategy for each of the 100 million Americans if few others give to asteroid protection (but not if sufficiently many give to asteroid protection).
b. Giving to asteroid protection is a dominant strategy for each of the 100 million Americans provided many others also give to asteroid protection.
c. Giving to asteroid protection is a dominant strategy for each of the 100 million Americans, regardless of how many others given to asteroid protection.
d. Buying jeans is a dominant strategy for each of the 100 million Americans, regardless of how many others given to asteroid protection.

Answer 1

Each American has the option to buy jeans or contribute towards asteroid protection. The dominant strategy depends on the number of people who choose each option. If many others give to asteroid protection, contributing towards asteroid protection is the dominant strategy.

Step-by-step explanation:

In this scenario, each of the 100 million Americans has two options: to buy a pair of jeans or to contribute $100 towards asteroid protection. The probability of an asteroid being deflected is equal to the proportion of Americans who contribute towards asteroid protection. Additionally, each American attaches a value of $1 to a 1% increase in the chance of asteroid deflection and a value of $100 to buying jeans instead of contributing towards asteroid protection.

To determine which strategy is dominant, we need to compare the payoffs for buying jeans and contributing towards asteroid protection based on the number of people who choose each option.

If few others give to asteroid protection, buying jeans would be a dominant strategy for each American because the value attached to jeans is $100, which is higher than the potential value attached to asteroid protection.

If many others give to asteroid protection, contributing towards asteroid protection becomes a dominant strategy for each American because the value attached to a 1% increase in the chance of asteroid deflection ($1) is higher than the value attached to buying jeans ($100).

Therefore, the correct statement is:

b. Giving to asteroid protection is a dominant strategy for each of the 100 million Americans provided many others also give to asteroid protection.