Games strategy refer task

REFER TASK:  

The Referred Coursework accounts for 100% of the module mark.

The deadline time for the submission of the Referred Coursework is Thursday 12 August 2021, 3.00 pm 

Work may be submitted on any date prior to the deadline. All assignments must be submitted electronically via the module site on Moodle. The file format has to be either MS Word or pdf. You can upload only one file.

Instructions

This is an individual piece of work.

The assignment consists of two questions. You must answer both questions.

Word Limit: You should write no more than 2,000 words per question (excluding references/data tables/diagrams), writing no more than 4,000 words in total. Include a word count at the end of each question.

The two questions carry equal marks.

• Include a reference section at the end of each question.

Good luck!

Questions

Question 1: (100 marks)

Does repeated interaction between the same players encourage cooperation in Prisoners’ Dilemma games?

As part of your answer to this question, you need to explain and analyse static, finitely repeated and infinitely repeated Prisoners’ Dilemma games and their equilibria. Consider both ‘simple’ and ‘modified’ Prisoners’ Dilemma games. The underlying game-theoretic concepts and methods need to be explained carefully and critically discussed.

Question 2: (100 marks)

Explain the difference between incomplete, imperfect, and asymmetric information in the context of game theory. Briefly outline four examples of games (real-life or hypothetical) characterised by:

complete and perfect information;complete and imperfect information;incomplete and perfect information; and • incomplete and imperfect information.

                                                                                                                                                                                                        (15 marks)

Consider two profit-maximising firms that form a duopoly market. Both firms produce the same homogenous product and are engaged in a Cournot quantity competition. Firm 1 and firm 2 choose simultaneously and non-cooperatively their output levels ??1 and ??2, respectively. The inverse market demand function is given by:

?? = 7 − 3(??1 + ??2),

where ?? is the price of the product. Firm 1’s and firm 2’s constant marginal costs of production are ??1 = 2 and ??2 = 3, respectively. Calculate the Nash equilibrium of this game as well as profits and market price. Carefully explain each step of your calculations and include economic interpretations. Use relevant diagrams to support

your arguments.                                                                                                                         (30 marks)

c) Assume now that firm 1’s marginal cost is still ??1 = 2, whereas firm 2’s marginal cost is ??2 = ??1 + ?? > 0, where ?? is a random variable that lies in the range [−??, ??] with a zero mean and distribution ??. Additionally, assume that ??1 ≥??, the true value of ?? is only known to firm 2, and both firms know ?? and distribution ??. Calculate the Bayes-Nash equilibrium of this game. There is no need to calculate firms’ profits or market price. Similarly to (b), carefully explain each step of your calculations and include economic interpretations. Use relevant diagrams to support your arguments.

                                                                                                      (40 marks)

d) Briefly compare and contrast your approach to solving (b) and (c).

                                                                                                                                        (15 marks)

Assessment Criteria

Marks will be awarded according to the following main criteria:

Achievement of the objectives of the questionAccurate explanation and use of relevant economic theories, concepts and methods Logical structure of the argumentsCritical analysis of relevant argumentsClarity of explanation – fluency of written exposition, grammar and correct spellingDemonstrated knowledge of the relevant literature and proper citation of sources.Keeping to the word limit, inclusion of word count.

Further Information

Work submitted within 24 hours of the due date will receive a mark, but it will be capped at the pass mark of 40%. Work that is submitted more than 24 hours after the official deadline will receive an automatic mark of zero. If you have valid extenuating circumstances for late work, the actual mark achieved will be recorded against that submission, no capping will apply. The additional 24 hours will run from the original hand in date and time to the next University working day.

Coursework including feedback will normally be returned within four working weeks of the due date.

Academic Offences

Academic offences, including plagiarism, are treated very seriously.  A student who is proven to have committed an academic offence may be placing his or her degree in jeopardy. It is your responsibility as a student to make sure that you understand what constitutes an academic offence, and in particular, what plagiarism is and how to avoid it. 

All your work must contain references to your sources, however acquired. To copy another person’s work is viewed as plagiarism and is not allowed in UK academic institutions. All your work must be your own and other sources must be identified as being theirs, not yours. The copying of another person’s work will result in you receiving a zero for your assignment and could result in expulsion from the university altogether.

Some useful guidance on how to reference correctly, and avoid plagiarism can be found on the following websites:

https://www.plymouth.ac.uk/student-life/your-studies/essentialinformation/regulations/plagiarism

http://www.learnhigher.ac.uk/referencing/  

Students are strongly recommended to self-review coursework prior to submission using the University’s Turnitin software. You can get information here. This tool assesses the originality of pieces of academic writing and detects potential academic offences such as plagiarism. The use of Turnitin is becoming standard practice at most UK universities as a way of ensuring academic standards. Plymouth Business School has introduced the sampling system following recommendations from our external examiners about the use of Turnitin. If you have any concerns about the use of Turnitin please contact your Programme Manager and/or personal tutor.

Extenuating Circumstances

If you have extenuating circumstances that prevent you from submitting your work on time or taking an exam, you will need to fill an extenuating circumstances form and submit corroborative evidence. If your extenuating circumstances for late work are deemed valid, you will receive the actual mark achieved (i.e. no capping will apply).

For further information on the Extenuating Circumstances Policy and Procedures, as well as the required form(s), check the Plymouth Business School UG Students’ Handbook, contact the Student Reception and/or check the following link:

https://www.plymouth.ac.uk/student-life/your-studies/essential-

information/exams/exam-rules-and-regulations/extenuating-circumstances

You are strongly advised to carefully pay attention to all additional University information and emails on the revision of the academic regulations pertaining to Extenuating Circumstances as a result of the current disruptions.

See module handbook for further information

REFER TASK:  

The Referred Coursework accounts for 100% of the module mark.

The deadline time for the submission of the Referred Coursework is Thursday 12 August 2021, 3.00 pm 

Work may be submitted on any date prior to the deadline. All assignments must be submitted electronically via the module site on Moodle. The file format has to be either MS Word or pdf. You can upload only one file.

Instructions

This is an individual piece of work.

The assignment consists of two questions. You must answer both questions.

Word Limit: You should write no more than 2,000 words per question (excluding references/data tables/diagrams), writing no more than 4,000 words in total. Include a word count at the end of each question.

The two questions carry equal marks.

• Include a reference section at the end of each question.

Good luck!

Questions

Question 1: (100 marks)

Does repeated interaction between the same players encourage cooperation in Prisoners’ Dilemma games?

As part of your answer to this question, you need to explain and analyse static, finitely repeated and infinitely repeated Prisoners’ Dilemma games and their equilibria. Consider both ‘simple’ and ‘modified’ Prisoners’ Dilemma games. The underlying game-theoretic concepts and methods need to be explained carefully and critically discussed.

Question 2: (100 marks)

Explain the difference between incomplete, imperfect, and asymmetric information in the context of game theory. Briefly outline four examples of games (real-life or hypothetical) characterised by:

complete and perfect information;complete and imperfect information;incomplete and perfect information; and • incomplete and imperfect information.

                                                                                                                                                                                                        (15 marks)

Consider two profit-maximising firms that form a duopoly market. Both firms produce the same homogenous product and are engaged in a Cournot quantity competition. Firm 1 and firm 2 choose simultaneously and non-cooperatively their output levels ??1 and ??2, respectively. The inverse market demand function is given by:

?? = 7 − 3(??1 + ??2),

where ?? is the price of the product. Firm 1’s and firm 2’s constant marginal costs of production are ??1 = 2 and ??2 = 3, respectively. Calculate the Nash equilibrium of this game as well as profits and market price. Carefully explain each step of your calculations and include economic interpretations. Use relevant diagrams to support

your arguments.                                                                                                                         (30 marks)

c) Assume now that firm 1’s marginal cost is still ??1 = 2, whereas firm 2’s marginal cost is ??2 = ??1 + ?? > 0, where ?? is a random variable that lies in the range [−??, ??] with a zero mean and distribution ??. Additionally, assume that ??1 ≥??, the true value of ?? is only known to firm 2, and both firms know ?? and distribution ??. Calculate the Bayes-Nash equilibrium of this game. There is no need to calculate firms’ profits or market price. Similarly to (b), carefully explain each step of your calculations and include economic interpretations. Use relevant diagrams to support your arguments.

                                                                                                      (40 marks)

d) Briefly compare and contrast your approach to solving (b) and (c).

                                                                                                                                        (15 marks)

Assessment Criteria

Marks will be awarded according to the following main criteria:

Achievement of the objectives of the questionAccurate explanation and use of relevant economic theories, concepts and methods Logical structure of the argumentsCritical analysis of relevant argumentsClarity of explanation – fluency of written exposition, grammar and correct spellingDemonstrated knowledge of the relevant literature and proper citation of sources.Keeping to the word limit, inclusion of word count.

Further Information

Work submitted within 24 hours of the due date will receive a mark, but it will be capped at the pass mark of 40%. Work that is submitted more than 24 hours after the official deadline will receive an automatic mark of zero. If you have valid extenuating circumstances for late work, the actual mark achieved will be recorded against that submission, no capping will apply. The additional 24 hours will run from the original hand in date and time to the next University working day.

Coursework including feedback will normally be returned within four working weeks of the due date.

Academic Offences

Academic offences, including plagiarism, are treated very seriously.  A student who is proven to have committed an academic offence may be placing his or her degree in jeopardy. It is your responsibility as a student to make sure that you understand what constitutes an academic offence, and in particular, what plagiarism is and how to avoid it. 

All your work must contain references to your sources, however acquired. To copy another person’s work is viewed as plagiarism and is not allowed in UK academic institutions. All your work must be your own and other sources must be identified as being theirs, not yours. The copying of another person’s work will result in you receiving a zero for your assignment and could result in expulsion from the university altogether.

Some useful guidance on how to reference correctly, and avoid plagiarism can be found on the following websites:

https://www.plymouth.ac.uk/student-life/your-studies/essentialinformation/regulations/plagiarism

http://www.learnhigher.ac.uk/referencing/  

Students are strongly recommended to self-review coursework prior to submission using the University’s Turnitin software. You can get information here. This tool assesses the originality of pieces of academic writing and detects potential academic offences such as plagiarism. The use of Turnitin is becoming standard practice at most UK universities as a way of ensuring academic standards. Plymouth Business School has introduced the sampling system following recommendations from our external examiners about the use of Turnitin. If you have any concerns about the use of Turnitin please contact your Programme Manager and/or personal tutor.

Extenuating Circumstances

If you have extenuating circumstances that prevent you from submitting your work on time or taking an exam, you will need to fill an extenuating circumstances form and submit corroborative evidence. If your extenuating circumstances for late work are deemed valid, you will receive the actual mark achieved (i.e. no capping will apply).

For further information on the Extenuating Circumstances Policy and Procedures, as well as the required form(s), check the Plymouth Business School UG Students’ Handbook, contact the Student Reception and/or check the following link:

https://www.plymouth.ac.uk/student-life/your-studies/essential-

information/exams/exam-rules-and-regulations/extenuating-circumstances

You are strongly advised to carefully pay attention to all additional University information and emails on the revision of the academic regulations pertaining to Extenuating Circumstances as a result of the current disruptions.

See module handbook for further information