Hello, could you please answer this question?

1. Suppose that there are 2 countries deciding whether to submit a proposal to host an international sporting event. It costs k > 0 to submit a proposal and the value of hosting the event to both countries is v > k. If country i submits a proposal then i must also choose the size of a bribe bi 0 to pay. The bribe is paid regardless of whether country i wins or not. When both countries submit a proposal, the country that pays the biggest bribe wins the right to host the tournament, and in the event that the bribes paid are the same size, each country wins with probability 1/2. If just one country submits a proposal that country wins and if no country submits a proposal then no one hosts the tournament.

(a) Are there any pure Nash equilibria of this game?

(b) Find a symmetric mixed strategy Nash equilibrium in which each country submits a proposal with probability 0 < p < 1 and, when submitting a proposal, each firm submits a bribe drawn from a continuous and atomless1 CDF F with support [0, v k]. Find F and p.