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 - de). (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, r, y and z in the matrix below. Erin 0 1 2 0, w 5.3 10.r Archibald 4,5 4,3 4,-3 6,10 y,3 z,-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. (c) 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. (1 point) What is/are Archibald's best response/s if Erin chooses a contribution level of 0? iii. (1 point) What is/are Archibald's best response/s if Erin chooses a contribution level of 1? iv. (1 point) What is/are Archibald's best response/s if Erin chooses a contribution level of 2? v. (3 points) Write down the subgame perfect Nash equilibria of this game