The bargaining game above (see Problem 4.2) is repeated with one difference: The outside body prohibits any agreement which gives player 2 a share of the pie below one-third. Find the Nash solution to...

The bargaining game above (see Problem 4.2) is repeated with one difference: The outside body prohibits any agreement which gives player 2 a share of the pie below one-third. Find the Nash solution to this bargaining problem.

Problem 4.2

Consider another two-person bargaining game. Player 1 has utility function given by u(x) = x where x∈(0,1) is the share of the pie that 1 will receive, leaving 1 − x for player 2, whose utility function is given as v(x) = (1 − x)^1/2. Suppose further that an outside body (the Law, an arbitration commission, the mafia etc.) prescribes that in case of non-agreement between players 1 and 2, player 2 will be awarded one-third of the pie while player 1 will receive nothing. Find the Nash solution to this bargaining problem.