Archibald Architecture and Erin's Engineers are two firms who are working together to build a new library for the local community. They must each contribute some amount of resources to the build: Archibald will contribute a units of resources at a cost of a, and Erin will contribute e units at a cost of 2e2. The final value of the build is 10(a + e - ae), which Archibald and Erin split equally, so that each receives a revenue of 5(a t e - ae). (a) (2 points) Write down Archibald and Erin's payoff functions. (b) (8 points) Suppose that the only resource contribution options available are 0, 1 and 2. Archibald and Erin must make their decisions simultaneously without consulting one an- other. i. Compute the payoffs that correspond to w, x, y and z in the matrix below. Erin 0 1 2 0 0,w 5,3 10,x Archibald 1 4,5 4,3 4,-3 2 6,10 y,3 2,-8 ii. Explain why (0,0) is not a Nash equilibrium in this game. iii. Identify Erin's two rationalisable strategies in this game. iv. In one sentence, explain why Erin's remaining strategy is not rationalisable. v. Write down the Nash equilibria of this game. No explanation is required. (c)* (4 points) Suppose now, that instead of being limited to three contribution levels, Archibald and Erin can contribute any non-negative amount of resources. Find the contribution made by each firm in the unique Nash equilibrium of this game