Econ 402 questions

HW2

September 5 2018

Due back in class by September 11 by 5 pm to Berk Idem.

1. (10 points)From Harrington, exercises at the end of chapter 2, # 15.

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2,3. (5 points each) From Harrington, exercises at the end of chapter 3, #3,4,

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4. (30) Construct the strategic form for the game trees in the two attached figures 1 and

2.

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5. (10) Each extensive form has a unique strategic form, but a given strategic form can

correspond to two or more extensive forms. Give an example to illustrate this.

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6. (25)) We consider a game with two players, A and B. The players each make one

decision, simultaneously with and independently of the other. Each chooses whether to

exert effort from the set of alternatives {0,1,2}. If the total effort exerted by the two players

is x, each player gets a payoffof (.9)(x).The cost of each unit of effort is borne by the player

exerting it and is equal to 1. Thus the payoff to a player who exerts y units of effort when

the total amount exerted is x is (.9)x−y. Write down the strategic form of this game, including the payoffs.

Is there a strictly dominant strategy?

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7. (15) Suppose there are two players, a manager and a worker. The manager decides

whether to hire the worker or not. If hired, the worker produces high or low output, which is

observed by the manager, who then has to decide whether to retain the worker or fire him.

Explain if "not hire" is a valid description of a strategy (in the sense of this class) for the

manager.

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