JUST ANSWER FROM PART B(IV) !!!THANKS Problem 2Archibald Architecture and Erin's Engineers are two firms that are working together to build a new li-brary for the local community. They must each contribute some amount of resources to the build: Archibaldwill contribute a units of resources at a cost of a², and Erin will contribute e units at a cost of 2e². Thefinal value of the build is 10(a + e-ae), which Archibald and Erin split equally, so that each receives arevenue of 5(a + e -ae).(a) Write down Archibald and Erin's payoff functions.(b) Suppose that the only resource contribution options available are 0,1 and 2. Archibald and Erinmust make their decisions simultaneously without consulting one another.i. Compute the payoffs that correspond to w, x, y and z in the matrix below.Erin15,3Archibald 01200, w4,54,36,10 y, 3210, x4, -32,-8ii. Is (0,0) is a Nash equilibrium in this game? Justify your assertion in no more than 25 words.iii. Is a resource contribution level of 2 rationalisable for Erin? Justify your assertion in no more than15 words.iv. Write down the two Nash equilibria of this game. No explanation is required.v. Suppose now, that instead of being limited to three contribution levels, Archibald and Erin cancontribute any non-negative amount of resources. Find the contribution made by each firm in the uniqueNash equilibrium of this game.(c) Now, suppose that Erin makes her decision first, and Archibald observes this decision before hemakes his decision. Let the only resource contribution options available be 0,1, and 2 again.i. Draw a game tree to represent this dynamic game.ii. What is/are Archibald's best response/s if Erin chooses a contribution level of 0 ?iii. What is/are Archibald's best response/s if Erin chooses a contribution level of 1 ?iv. What is/are Archibald's best response/s if Erin chooses a contribution level of 2 ?v. Write down the subgame perfect Nash equilibria of this game.

Nash equilibrium is defined as that point from which no player is willing to deviate given all the…

Archibald Architecture and Erin's Engineers are two firms that are working together to build a new li- brary 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 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 + e- ae). (a) 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

Archibald Architecture and Erin's Engineers are two firms that are working together to build a new li- brary 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 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 + e- ae). (a) 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

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Chapter1: Making Economics Decisions

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JUST ANSWER FROM PART B(IV) !!!THANKS

Problem 2
Archibald Architecture and Erin's Engineers are two firms that are working together to build a new li-
brary 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 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 + e -ae).
(a) 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. Compute the payoffs that correspond to w, x, y and z in the matrix below.
Erin
1
5,3
Archibald 0
1
2
0
0, w
4,5
4,3
6,10 y, 3
2
10, x
4, -3
2,-8
ii. Is (0,0) is a Nash equilibrium in this game? Justify your assertion in no more than 25 words.
iii. Is a resource contribution level of 2 rationalisable for Erin? Justify your assertion in no more than
15 words.
iv. Write down the two Nash equilibria of this game. No explanation is required.
v. 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. Draw a game tree to represent this dynamic game.
ii. What is/are Archibald's best response/s if Erin chooses a contribution level of 0 ?
iii. What is/are Archibald's best response/s if Erin chooses a contribution level of 1 ?
iv. What is/are Archibald's best response/s if Erin chooses a contribution level of 2 ?
v. Write down the subgame perfect Nash equilibria of this game.

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