Strategic Games for Business Final Examination ECON1340

EXAM DETAILS

Course Code: ECON1340

Course Description: Strategic games for business

Total number of pages (incl. this cover sheet):

ALLOWABLE MATERIALS AND INSTRUCTIONS TO CANDIDATES

Read the instructions provided carefully before you start the exam. The instructions are available on Canvas-> Assignments -> Assessment 3

Write your full name and student number on the exam booklet together with the number of pages used.

There is a strict page limit of two pages per answers to each question (font size 12pt)

Commence each question on a new page.

Once you finished writing, save the word file and upload it via the link provided on Canvas-> Assignments -> Assessment 3

This assignment includes three multi-part questions. You are required to answer all questions.

This assignment is worth 50 marks and comprises 50% of the total marks allocated to this course.

Question 1: Consider two students working together on a group assignment for a Game Theory course. Student 1 is grade focussed and wants to do well in the course but considers effort costly and prefers less work to more. Student 2 might be either studious or lazy with equal probability. If student 2 is studious then they care both about grades and learning. If student 2 is lazy then they value grades but hates work. As long as someone does the work then they will do well in the project. Both students have the option of working (W) on the project this weekend or going to a party (P) and must make the decision independently without observing the other's choice. The payoffs for student 1 and each type of student 2 are as follows.

Draw the extensive form of this game. (4 Marks)

Draw the three-player normal form game after the Bayesian transformation and define payoffs for each of the three players (student 1, student 2 studious and student 2 lazy). (5 Marks)

Find the set of Bayesian Nash equilibrium of this game. (6 Marks)

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Question 2: Apple and Samsung are the only two producers of smartphones in Australia. Every year they set the price of their phones for the rest of the year. Suppose they can either price their phones Low or High. If one company set the price Low and the other set it High, then the low-price company would receive a profit equal to 400 while the company with the high price only receives 100. If they both set the price low they both receive 200. Finally, if the both decide to set their prices high the each receive 300.

What is the Nash equilibrium of this game if it is only played once? (5 marks)

What is the subgame perfect equilibrium of this game if both firms play the same game for T periods? (5 marks)

Suppose in 10 years AI would replace smart phones and both companies go bankrupt. However currently neither of the two firms know what will happen in 10 years from now and have no expectation about this possibility. Is it possible to support an equilibrium in which both firms set a high price in all periods? (7 marks)

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Question 3: A manufacturing company is looking to hire an agent to manage a new project. The agent can exert a high effort ()or low effort (). The high effort increases the probability of project success, but it is more costly for the agent. The company wants to design a contract that ensures the agent will choose to exert high effort and will also be willing to accept the job.

If the agent exerts high effort (), the probability of success is 0.8. If the agent exerts low effort ( ), the probability of success is 0.4. The agent's cost of exerting high effort is = 10, and the cost of exerting low effort is =2.

The company's payoff is 100 if the project is successful and 0 if it is not. The agent's utility is given by: = , i.e. their wage minus their effort cost. The agent has an outside option with a utility of 5.

Design a contract (, ) where is the wage if the project is successful and is the wage if the project fails. Write down the incentive compatibility and participation condition that ensures the agent will accept the contract and choose to exert high effort. (8 Marks)

Solve the conditions from (a) and find the optimal contract with two sets of payments such that the agent will accept the contract and choose to exert high effort. (8 Marks)

What is the companys expected profits under such contract? (2 Marks)

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