3. (16 points) 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 a2, and Erin will contribute units at a cost of 2. The final value of the build is 10(a + ae). which Archibald and Erin split equally. so that each receives a revenue of 5(a + e ae). a. (2 points) Write down Archibald and Erin's payoff functions. b. (9 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 another. i. (2 points) Compute the payoffs that correspond to w. x. v and z in the matrix below. Archibald ii. (2 points) Is (0,0) is a Nash equilibrium in this game? Justify your assertion in no more than 25 words. iii. (2 points) Write down the two Nash equilibria of this game. No explanation is required. iv. (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 unigue Nash equilibrium of this game. . (5 points) Now, suppose that Erin makes her decision first, and Archibald observes this decision before he makes his decision. Let the only resource contribution options available be 0, 1, and 2 again. i. (2 points) Draw a game tree to represent this dynamic game. ii. (3 points) Write down the unigue subgame perfect Nash equilibrium of this game