MAST30022决策

MAST30022 Decision Making
Assignment 4, Semester 1 2022
Due time: 4pm, Friday 26 August.
Name:
Student ID:
To complete this assignment, you need to write your solutions into the blank answerspaces following each question in this assignment PDF.If you have a printer (or can access one), then you must print out the assignmenttemplate and handwrite your solutions into the answer spaces.If you do not have a printer but you can figure out how to annotate a PDF usingan iPad/Android tablet/Graphics tablet orusing Adobe Acrobat, then annotate youranswers directly onto the assignment PDF and save a copy forsubmission.Failing both of these methods, you may handwrite your answers as normal on blankpaper and then scan for submission (but note that you will thereby miss valuablepractice for the exam process). In that case, however, your document should have
the same length as the assignment template otherwise Gradescope will reject yoursubmission. So you will need to add as many blank pages asnecessary to reach thatcriterion.Scan your assignment to a PDF file using your mobile phone (we recommend Cam-Scanner App), then upload by going to the Assignments menu on Canvas and submitthe PDF to the GradeScope tool by firstselecting your PDF file and then clicking on‘Upload PDF’.– it is a single pdf with all pages in correct template order and the correct way up,and with any blank pages withadditionalworking added only at the end of the

template pages;

– has all pages clearly readable;
– has all pages cropped to the A4 borders of the original page and is imaged from
directly above to avoid excessive ’keystoning’
These requirements are easy to meet if you use a scanning app on your phone and take
some care with your submission - please review it before submitting to double check
you have satisfied all of the above requirements.
MAST30022 Semester 2, 2022 Assignment 1 1
The submission deadline is 4pm Melbourne time on Friday 26 August. Youhave longer than of the normal one week to complete this assignment. Late submissionwithin 20 hours after the deadline will be penalised by 5% of the total available marksfor every hour or part thereof after the deadline. After that, the Gradescope submission
channel will be closed, and your submission will no longer be accepted. We recommendyou submit at least a day before the due date to avoid any technical delays. If thereare extenuating, eg medical circumstances, contact the Subject Coordinator, Dr MarkFackrell.
There are 4 questions, of which 2 randomly chosen questions will be marked. Noteyou are expected to submit answers to all questions, otherwise a mark penalty willapply.Working and reasoning must be given to obtain full credit. Give clear and conciseexplanations. Clarity, neatness, and style count.
MAST30022 Semester 2, 2022 Assignment 1

1. Consider the game in extensive form shown in Figure 1 in which Player 1 owns vertices
   Figure 1: Game in extensive form for Question 1
   For vertex x ∈ {a, b, c, d, e, f, g}, use the label Lx if the left hand edge is chosen, Rx ifthe right hand edge is chosen, and Cx if there is only one possible move.(a) Redraw the game in extensive form labelling all the edges accordingly.
   MAST30022 Semester 2, 2022 Assignment 1 3
   (b) Describe the strategy set for each player, give the normal form of the game, and
   find any pairs of pure strategies in equilibrium if the game is of
   (i) perfect information;MAST30022 Semester 2, 2022 Assignment 1 4
   (ii) imperfect information and Player 2 cannot distinguish between vertices b andc, and Player 1 cannot distinguish between vertices d and e.
   MAST30022 Semester 2, 2022 Assignment 1 5
2. Consider the game with chance moves in extensive form shown in Figure 2 in whichPlayer 1 cannot distinguish between the two vertices s/he owns. Describe the strategyset for each player and give the normal form of the game where the payoffs are expectedpayoffs.C represents Chance or Nature.Find all pairs of Nash equilibria in pure strategies, if they exist.Figure 2: Game with chance moves in extensive formYou may continue your answer on the next page.MAST30022 Semester 2, 2022 Assignment 1 6MAST30022 Semester 2, 2022 Assignment 1 7
3. Consider the following two-person zero-sum game
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