Consider the following bargaining problem. In the usual way, a "unit pie" is split into non-negative amounts \(x\) and \(y\) with \(x+y \leq 1\). The utility function of player \(\mathrm{I}\) is \(u(x)=x\), the utility function of player II is \(v(y)=1-(1-y)^{2}\). The threat point is \((0,0)\).

(a) Draw the bargaining set (as set of possible utilities \((u, v)\) ) and indicate the Pareto-frontier in your drawing.

(b) Find the Nash bargaining solution. How will the pie be split, and what are the utilities of the players?