1. Consider a model of a society made up of N = 100 people. Each individual must decide whether to be tolerant (T) or intolerant (I). All else equal, everyone likes being tolerant better than being intolerant. In particular, an individual who behaves tolerantly gets a utility gain of 20 and an individual who behaves intolerantly gets a utility gain of 0.

In addition, people like to fit in. As a result, they gain benefits the more people behave like them. If n other people behave in the same way as person i, then she gets an extra payoff of n. (Note 0 n 99.)

Suppose, then, that person i believes n_T other people will behave tolerantly, with 0 n_T 99 and n_I other people will behave intolerantly. (Notice, this implies n_I = 99 n_T.) Person is payoff from behaving tolerantly is

u_i(T,n_T,n_I) = 20 + n_T.

Person is payoff from behaving intolerantly is

u_i(I,n_T,n_I) = n_I = 99 n_T.

1. 1. For what values of n_T is it a best response for person i to behave tolerantly? For what values of n_T is it a best response for person i to behave intolerantly? ( Note that n_T must be a whole number.)
2. 1. Is there a Nash equilibrium where everyone behaves tolerantly? Is there a Nash equilibrium where everyone behaves intolerantly?
   2. Write down the utilitarian payoff for society for all equilibria identified in ( b ).
   3. In what sense does this model illustrate one of our social dilemmas? Give an example of a real world phenomenon not discussed in class that this model might be a good analogy for.
   4. Is this a setting in which an effective policy response is likely to require ongoing or short-run intervention by the government?