1. It's August, 1914. The Central Powers and the Allies are playing the game of \"chicken,\" with the following material payoffs: dare chicken dare -3, -3 1, -1 chicken -1, 1 U, U The interpretation of these material payoffs is as follows. Each side can either \"dare\" to commit to war, or \"chicken out\" and give in to the other side's demands but avoiding war. If both sides dare, a disastrous war follows. If one side dares and the other chickens out, the daring side gains in imperial power at the expense of the other side. If both chicken out1 the status quo remains. (a) [5pts] What are the pure-strategg,r Nash equilibria of the above game? What is the implication of these equilibria for how the conict would have played out if leaders of both sides only cared about material outcomes? (b) [l5pts] Now suppose the two sides have the following distributional preferences over material outcomes m1 and 72: U1 (71, 712) = 71 - 0.6(#1 - 72) if m1 2 72 W1 (71, 72) = 71 - 0.8(72 - m1) if m1