Two construction companies are lobbying to obtain a share of work on repaving city streets. The share of the project going to each firm depends on money contributions to the mayor's reelection fund. The project has value V in total. The mayor is somewhat biased in favor of firm 1, which is run by his niece. If firm 1 contributes x1 and firm 2 contributes x2, then the shares of the project going to firms 1 and 2 are s1 and s2, respectively, where
s1(x1,x2) = (2x1)/(2x1 + x2) and s2(x1,x2) = (x2)/(2x1 + x2);
The payoff to firm i is
πi(x1,x2) = si(x1, x2)V - xi, i = 1, 2.
Calculate the Nash equilibrium contributions for each firm if they make contributions simultaneously.