Archibald Architecture and Erin's Engineers are two firms that 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 2e". 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) Suppose that the only resource contribution options available are 0, 1 and 2. Archibald and Erin must make their decisions simultaneously without consulting one another. i. (2 points) 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. (2 points) Is (0,0) is a Nash equilibrium in this game? Justify your assertion in no more than 25 words. iii. (1 point) Is a resource contribution level of 2 rationalisable for Erin? Justify your assertion in no more than 15 words. iv. (2 points) Write down the two Nash equilibria of this game. No explanation is re- quired. v. (3 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