University of Technology Sydney · FACULTY OF ECONOMICS

23506 Chap.13 Final Exam Playbook: Question Structure, 120-Minute Pacing and the Practice Exam Walkthrough

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Chapter 13 of 13 · 23506

Final Exam Playbook: Question Structure, 120-Minute Pacing and the Practice Exam Walkthrough

The available final guidance says: Online, closed book, AI invigilated, and 120 min. It permits blank papers, a pen and a non-programmable calculator and describes about 20 questions. Dividing two hours by about 20 gives a derived average of roughly six minutes per question, not a mandated allocation. Short true-or-false items should create time for mixed matrices, trees and multi-part applications. Current official instructions and the subject outline govern administration; no examination date is inferred here.

Classify before calculating. Dominance prompts need comparisons holding opponents fixed; all-Nash prompts need pure scans and plausible mixed supports; SPE prompts need information sets, subgames and complete strategies; probability prompts need expected value and boundary cases; bargaining starts from terminal rejection value; repeated games compare obedience with a one-time deviation and then verify punishment. Show the decisive comparison even if final arithmetic must be revisited.

The practice review’s 2b and 2d mixed vectors are re-solved from their payoff matrices. For 2b the equilibrium is ((1/3,2/3),(3/4,1/4)). For 2d, eliminate Row U and then Column L; the remaining support gives ((0,1/2,1/2),(0,3/5,2/5)). The demand-game review establishes total simultaneous equilibrium demand 100, equal division at 100/3 each, and a sequential outcome (100,0,0). A final audit checks every minus sign, probability sum, fraction bar, weak inequality, tuple order and the noun requested by the question.

In this chapter

What this chapter covers

01Final conditions and flexible pacing
02Question-family triage
03True-or-false proof method
04Practice matrices 2a and 2c
05Practice matrices 2b and 2d re-solutions
06Demand-game, tree and calculation audits

Worked example · free

Practice-final 2d re-solution

Q. Rows U,M,D; columns L,M,R. Payoffs: U=(1,5),(1,5),(1,2); M=(4,0),(4,1),(2,3); D=(2,0),(2,4),(5,2). Find the mixed equilibrium. Illustrative - not an official mark allocation.

Show that Row U is strictly dominated and remove it.
In the surviving rows, show Column L is strictly dominated and remove it.
Make Column indifferent between M and R to solve Row’s support probability.
Make Row indifferent between M and D to solve Column’s support probability.
Restore zero coordinates and verify excluded actions earn less.

Row M strictly dominates U. With rows M,D, Column L pays zero against either row and is strictly dominated. Let p be Row’s probability of M. Column indifference gives p+4(1−p)=3p+2(1−p), so p=1/2. Let q be Column’s probability of M. Row indifference gives 4q+2(1−q)=2q+5(1−q), so q=3/5. The full equilibrium is ((0,1/2,1/2),(0,3/5,2/5)). Excluded U earns 1 below 16/5, and excluded L earns 0 below 5/2.

Sia tip — If an expected-payoff equation cannot cross, recheck payoff ownership before changing the support.

Glossary

Key terms

Triage: Rapidly classifying a question so the correct solution algorithm starts immediately.
Pacing baseline: A derived average used to monitor time, not a required per-question limit.
Safety-net question: The review’s label for foundational concept, normal-form and extensive-form checks.
Method mark: Credit supported by a correct setup or strategic comparison even before a final number.
Independent verification: Checking a result through substitution, a deviation test, domain or payoff identity.
Complete object: The exact requested output, such as all equilibria, a strategy profile, path, threshold or payoff.

FAQ

Final Exam Playbook: Question Structure, 120-Minute Pacing and the Practice Exam Walkthrough FAQ

How long is the final?

The available wording states 120 minutes.

What are the conditions?

Online, closed book, AI invigilated, and 120 min.

What may be used?

The review permits blank papers, a pen and a non-programmable calculator; follow current official instructions.

How many questions are expected?

The review says about 20, so roughly six minutes each is only a planning average.

What does the review cover?

True-or-false concepts, dominance, iterated elimination, pure and mixed Nash equilibrium, subgames, strategies, SPE and applications.

What is practice 2b’s mixed vector?

((1/3,2/3),(3/4,1/4)) in row order U,D and column order L,R.

What is practice 2d’s mixed vector?

((0,1/2,1/2),(0,3/5,2/5)) in orders U,M,D and L,M,R.

What is total demand in simultaneous demand equilibrium?

Compatible equilibrium claims total 100; equal division at 100/3 each is one equilibrium.

What is the sequential demand outcome?

Backward induction gives (100,0,0) under the stated remainder-taking rule.

Is there an exam hurdle?

A hurdle is not stated — confirm in the subject outline. The 50% weight alone is not a separate hurdle statement.

What should the final ten-minute audit cover?

Re-read the command word and confirm you delivered the requested object: all equilibria, a complete strategy, an outcome, a threshold or an explanation. In matrices, verify ordered-pair ownership, all tied best responses, probability vectors summing to one and equal expected payoffs for every supported action. In reduced games, restore deleted actions with probability zero and test that none earns more. In trees, confirm information sets, the whole-game subgame count, tuple order, off-path actions and the distinction between profile and path. In Nature problems, substitute the equality cutoff into the original expected payoffs and check interval endpoints. In bargaining, count delays from the current decision date and ensure immediate agreement shares sum to the stated pie. In repeated games, include the current temptation, the leading discount on next-period punishment and a credibility check after a dirty history. Circle minus signs and fraction bars. Finally confirm current official submission instructions; this guide supplies no examination date and no unstated hurdle.

Study strategy

Exam move

Use two-pass timed sets. Scan and classify every question, then bank direct definitions and pure-response checks before returning to lengthy calculations. On blank paper, use compact ledgers: response arrows for matrices, node/action/value for trees, and follow/deviate streams for repetition. Re-solve practice 2b and 2d from payoffs until fraction bars and probability ownership are automatic. For true-or-false, identify the exact universal word or reversed concept and provide one decisive sentence. Reserve a final audit for all requested parts, player order, strategy completeness, probability totals, support payoffs, threshold equality, discount timing and minus signs. Confirm official operational details in the subject outline rather than relying on any unstated date or rule.

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