Say that there are two donors considering whom to back in the upcoming presidential primary: either candidate AOC or candidate CB. Both donors want party unity, in which both donors back the same candidate. However, donor 1 would rather the party unite around AOC rather than CB, while donor 2 would rather the party unite around CB. For both donors, a fractured party (a party where people differ on whom they support) is the worst thing.
a; Say that donor 1 chooses whom to back first. Then donor 2 makes their choice. Model this as an extensive form game. For donor 1, use the payoffs 0, 1, 2. For donor 2, use the payoffs 0, 1, 2. Find all (pure strategy) Nash equilibria of this game. Write down which of these Nash equilibria are subgame perfect. In your opinion, is it better to be the donor who
goes first (donor 1) or the donor who goes second (donor 2)?
b; Now say that there are three donors, and again each donor chooses whether to back AOC or CB. Again, donor 1 would rather the party unite around AOC rather than CB, while donor 2 would rather the party unite around CB, and for both donors, a fractured party is the worst thing. The third donor is most concerned that CB gets at least some support: the worst thing for donor 3 is if CB gets no support at all. Otherwise, donor 3 would like to have party unity also. Donor 1 goes first, then donor 2, and then donor 3. Model this as an extensive form game. For donor 1, use the payoffs 0, 1, 2. For donor 2, use the payoffs 0, 1, 2. For donor 3, use the payoffs 0, 1, 2. Find a subgame perfect Nash equilibrium of this game (you don’t have to write down all of them).
