Strategic Interaction and Signaling in Labor Market

QUESTION 1

Consider the following simultaneous move strategic interaction between Lisa and Anne, where they can agree on a course of action or not.

(a) For what values of  does this game have a unique Nash equilibrium? What is that equilibrium?

(b) For what values of  does this become an assurance (coordination) game?

QUESTION 2

This question pertains to signaling in the labour market. Suppose students come in two types: highly competent and less competent. Both types of students can get university degree, but for the less competent type getting a university degree takes extra time and effort:

· Highly competent students have to spend N years to graduate from university.

· Less competent students take three times as long.

Students with university degrees can earn 81 (thousand dollars) each year working, whereas without a degree they can earn only 36 (thousand dollars) each year. Most companies would not hire them.

Each type of student gets a payoff equal to , where S is the salary measured in thousands of dollars and N is the number of years spent getting a university degree.

(a) What is the range of values for N for which a highly competent student will choose to get a university degree?

(b) What is the range of values for N for which a less competent student will choose to get a university degree?

(c) What is the range of values of N for which a highly competent student will choose to get a university degree to signal their competence, but a less competent student will not?

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QUESTION 3

This question pertains to how individuals deal with risky situations and interact with others in similar situations to mitigate risk.

Suppose you invest in a business with risky returns:

· With probability 0.6 you have good luck and earn $14,400

· With probability 0.4 you have bad luck and earn $6,400.

Suppose your friend has a sure income of $14,400. She offers to provide you with an insurance contract:

· If you have good luck you pay her $x

· If you have bad luck she makes you a payment so that your income is $10,000

Both of you have Utility from income:  =

a) What is the minimum value of x (to the nearest dollar) such that your friend will provide you with insurance? (Hint: think about your friend’s expected utility.)

Question 2

b) What is the maximum value of x (to the nearest dollar) for which you will accept your friend’s offer? (Hint: think about your expected utility.)

(5 + 5 = 10 marks)

QUESTION 4

Joe, Rob, and Andy are treasure hunters. They find 1000 gold coins.

Rob has first choice from the three bags of coins. Andy then gets to choose from the remaining two bags, before Joe receives the final bag.

The two potential divisions of the gold coins are as follows:

(i) 250, 350, 400  

(ii) 200, 300, 500

Each person’s payoff is the number of coins that he gets.

(a) Using backward induction, briefly describe the outcome of this game under both scenarios. Who will receive which bag of coins?

(b) If Joe could choose how to divide the coins into three bags, what division would he choose? (He still receives the last bag of coins, with Rob and Andy choosing before him.)  

(5 + 3 = 8 marks)

QUESTION 5

Consider a strategic interaction between two tech companies: Orange and Airsoft. Both of them have to decide whether to invest in two competing nascent robot technologies: I-bot or N-bot.

· If both invest in I-bot, Orange gets 40 and Airsoft gets 100.

· If both invest in N-bot, then Orange gets 40 and Airsoft gets 70.

· If Orange invests in I-bot and Airsoft invests in N-bot, Orange gets 90 and Airsoft gets 60.

· If Orange invests in N-bot and Airsoft invests in I-bot then their payoffs ae 50 and 60 respectively.

You have been hired by the CEO of Orange to provide her with all the alternative options with regards to this interaction, including her best strategic response.

(a) Represent this game in its normal form (played simultaneously), clearly labelling the

      players, their strategies and pay-offs.

(b)  Verify that that there is no pure strategy Nash Equilibrium in this game.

(c) What is the maximum profit each company can guarantee from playing each of their pure strategies?

(d) Find the mixed strategy Nash Equilibrium in this game and interpret each player’s equilibrium strategy.

(e) Outline how the CEOs of each company would operationalise this mixed strategy in order for it to be successful?

(f) Given that both players are playing according to their mixed strategies, what is their expected profit? Are the expected profits higher than the maximum guaranteed profits reported in part (c)?