(10 points) The Quebec provincial government is to decide whether to extend the Metro "Blue" line from St-Michel to Anjou. The values of the extension for people living in St-Michel and Anjou are a and b respectively. The cost of construction is c > 0. The Government wants to go ahead with the construction if and only if a + b 2 c. The values a and b are known by the residents of St-Michel and Anjou but not by the Government; c is known to everybody. To learn these values the Government asks each neighbourhood (St-Michel and Anjou) to submit the value of the construction to the locality. Given the submitted valuations . and vo, which need to be non-negative, the Government constructs the bridge if and only if v. + v. 2 c, and tax St-Michel and Anjou ta(va, Us) and to(Va, Us) respectively, where ta(va, Ub) = Jc - Up if va tu > c and us