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Assignment 1
Instructions: Provide clear, comprehensive and succinct answers to the following problem set. The CRA sheet below provides further guidelines regarding what is expected. Be sure to attach the CRA sheet to your assignment, which should be submitted online by the 27th of April 2021. The link for online submission will be in the Assessment section on the Blackboard site for the unit.

1. (20 points) Solve problems U2 and U3 from Chapter 3 of the textbook
2. (25 points) Consider the following game, which illustrates Nobel Laureate Thomas Schelling’s solution to the problem of how a kidnapped person can induce a kidnapper to release him after the person has learned the identity of the kidnapper.

The game starts off with the kidnapper, say Alex, deciding whether or not to kidnap Bart. If he decides not to kidnap Bart, the game ends. Alex gets a payoff of 3, while Bart receives a payoff of 5. However, if Alex decides to go through with the kidnapping, he is successful, but there is a scuffle in which he is unmasked, so that his identity is revealed to Bart. This creates another problem for Bart, since Alex would now be inclined to kill Bart since Bart, if released could identify Alex to the police. Bart then decides whether to reveal something compromising/incriminating about himself to Alex that is not known to the rest of the world. (For example, he could have embezzled funds from the company he works in or has had an extramarital affair his wife does not know about. Effectively, he is offering this secret as a “collateral” which Alex can use to ensure his silence). Whether or not Bart decides to tell his secret, Alex has to decide to either kill him or release him. If he kills Bart the game ends and payoffs to Alex and Bart are respectively 4 and 0. If he releases Bart, then Bart has to decide whether to tell the police or not. If Bart does not tell the police the game ends and payoffs to Alex and Bart are respectively 5 and 2. If Bart chooses to tell the police, however, there are two scenarios to consider. If he hasn’t revealed his incriminating secret to Alex, the game ends and the payoffs to Alex and Bart are 1 and 4 respectively. But if he has revealed his secret to Alex, then Alex has to decide whether to reveal that secret to the world. If he does then the game ends and payoffs are 2 to Alex and 1 to Bart. If he doesn’t the game ends with payoff of 1 to Alex and 3 to Bart.

(a) Draw the extensive (tree) form of the game. How many strategies do Alex and Bart have? Write them down. {Hint: In doing so do not forget that a strategy is a complete plan of action.}
(b) Now present the game in strategic form. {Hint: The payoff table is pretty big! ? } Identify all of the Nash equilibria in this game.

(c) Which of these equilibria is the subgame perfect Nash Equilibrium (SPNE)? Explain and illustrate your answer using backward induction on the game tree.
(d) Pick any two of the other Nash equilibria that are not SPNE. Discuss the credibility problems associated with these equilibria.

3. (25 points) Consider the games of Prisoner’s Dilemma, Assurance, Chicken and Battle of Cultures discussed in the lecture on simultaneous move games. While the structure of these games can “fit” many situations, in this exercise think of them as games applying to teamwork. Specifically, imagine there are two players working on a future assignment for EFB337 they have to submit jointly as a two-person group assignment. However, the process of completing this assignment can be modelled as a game in which each player has two strategies, one in which they “Shirk” and do not contribute much to the assignment and one in which they “Work” and contribute a lot of effort into the assignment.

(i) Describe the teamwork game in two different forms, choosing any two structures from Prisoner’s dilemma, Assurance, Chicken and Battle of Cultures. Each case obviously describes a different type of teamwork. Your description should clearly capture the nature of the interaction and the context for each game in an intuitive and meaningful way.

(ii) In your chosen cases discuss any “solutions” to the teamwork problem. That is, are there any strategic moves (as defined in chapter 9) that can be made to ensure that both players choose to work hard? Can you think of other ways in which the problem can be resolved?
(Hint: Think about focal points, mechanisms relating to repeated games, reputation, strategic moves and credibility. Apart from discussions in Chapter 4 and 9 reading a bit wider and deeper into the textbook will help. For example, the chapter 10 on the prisoner’s dilemma and chapter 11 on collective action games are also relevant).

(iii) Based on your experience/intuition, describe an alternative way of characterizing the teamwork game. That is, create a game that fits your view of how the teamwork situation plays out (distinct from any of the standard structures discussed above)

4. (15 points) Read section 4A of Chapter 7 and attempt U5 from the same chapter.
5. (15 points) Brisbane Organic Products (BOP) is planning to introduce a new flavour of coconut oil – Ginger – to the market. If they introduce this flavour and there is strong demand (the probability of which is 0.5) they will make net earnings of $250,000. However, with weak demand (probability 0.5) they will only make $40,000. If they do nothing the payoff is $0.

(a) Assume that BOP’s utility function is characterized by the function where I is net earnings from any venture. Will BOP introduce the Ginger flavour? Explain your answer based on the expected utility model.

(b) Now suppose market research department of BOP provides the CEO the new information that introducing the Garlic flavour in coconut oil will bring a certain return of $100,000. However, BOP has only enough resources to launch one new flavour. Which flavour – Ginger or Garlic – will BOP introduce? How much would the certain return from Garlic have to be to make BOP indifferent between the two options?

(c) How would your answers to (b) change if the utility function characterizing BOP was ? Explain and interpret your answer.

 

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