23506 Strategic Decision Making and Game Theory
The Complete Exam Bible · Spring 2026Strategic Decision Making and Game Theory
23506 studies decisions whose consequences depend on what other decision makers choose. The subject begins by translating a strategic situation into players, feasible strategies, profiles and ordered payoffs. Normal-form matrices make simultaneous incentives visible: a best response maximises a player’s payoff against a fixed opposing action; strict or weak dominance compares one strategy against every opposing action; and Nash equilibrium requires every chosen strategy to be a best response. Classic Prisoner’s Dilemma, Battle of the Sexes, Stag Hunt, Chicken and cyclic examples develop conflict, coordination and selection intuition without letting a familiar story replace the displayed numbers.
The middle of the subject applies those tools to demand, auctions, Cournot quantities, Bertrand prices and market entry. Mixed strategy then makes uncertainty strategic. A player randomises only when supported actions are tied at the maximum expected payoff. Crucially, one player’s probability is found from the other player’s indifference. Entry, tennis and detective applications show why equilibrium frequencies manage congestion, predictability or targeting rather than merely reflecting an action’s intrinsic quality.
Extensive-form games add time and information. A strategy becomes a complete plan covering every information set, including branches that do not occur. A proper subgame begins at a singleton decision node and cannot cut an information set. Subgame-perfect equilibrium requires Nash equilibrium in every subgame, so backward induction removes threats that would not be optimal if reached. Stackelberg quantity leadership shows how credible commitment changes a follower’s response; chance nodes show when expected value belongs before rather than after a state is observed. Probability equality points are retained because indifference can enlarge the SPE set.
The later subject tests the reach of backward reasoning. Forward induction uses an observed sacrifice to infer a surviving intention. Trust and centipede games separate a formally correct selfish-payoff SPE from observed cooperation or efficiency. The chain-store paradox shows why complete-information finite reasoning rejects deterrence and why a reputation account requires uncertainty about type. Sequential bargaining converts rejection into a discounted reservation value: the proposer offers exactly enough for acceptance under the stated equality rule. Infinite repetition converts future reward and punishment into current incentives; finite repetition instead unravels from a known last period.
The mathematical toolkit is integrated throughout. Intervals preserve strict regions and equality cases; expectation weights unresolved states; argmax returns every tied maximiser; and discount exponents count delays from the evaluation date. The guide keeps exact fractions, re-derives visually compressed probability vectors from the underlying matrices and labels all worked solutions as AskSia-authored. It does not infer a due date, quiz window or examination date because the subject outline is unavailable.
What 23506 covers
23506 moves from strategic representation and classic 2×2 games through best response, dominance, pure and mixed Nash equilibrium, then turns to game trees, subgame perfection, leadership, Nature, forward induction, bargaining and repeated cooperation. The final chapters consolidate the mathematical toolkit and apply it to the supplied 120-minute practice-review structure.
How 23506 is assessed
| Component | Weight | Format |
|---|---|---|
| Online quizzes | 40% | Five quizzes; the best four marks out of five count toward the final mark. |
| Online experiments | 10% | Two experiments; the available overview says there is no correct answer and completion is the relevant engagement. |
| Final exam | 50% | Online, closed book, AI invigilated, and 120 min. |
The review material permits blank papers, a pen and a non-programmable calculator. About 20 questions are described. A hurdle is not stated — confirm in the subject outline. No assessment or examination date is inferred here.
Free equilibrium drill: from matrix to complete mixed answer
- 2Mark Row’s response to each column and Column’s response to each row; establish that no cell is mutually marked.
- 2Let p be Row’s probability of U and equate Column’s expected payoff from L and R.
- 2Let q be Column’s probability of L and equate Row’s expected payoff from U and D.
- 2Solve exact fractions, attach them to the printed action order and verify both vectors sum to one.
- 2Substitute the probabilities back into each pair of supported expected payoffs and state the equilibrium set.
Key terms
- Best response
- An action or set of actions maximising a player’s payoff against fixed opposing strategies.
- Strict dominance
- A strategy gives a strictly higher payoff than another against every opposing strategy.
- Nash equilibrium
- A strategy profile in which every player is choosing a best response to the others.
- Mixed strategy
- A probability distribution over a player’s pure strategies.
- Information set
- Decision nodes a player cannot distinguish when choosing an action.
- Subgame-perfect equilibrium
- A strategy profile inducing Nash equilibrium in the whole game and every proper subgame.
- Discount factor
- A number δ in (0,1) multiplying value for each one-period delay.
- Trigger strategy
- A history-contingent plan that begins cooperatively and activates punishment after a specified event.
23506 FAQ
What are the assessment weights?
Five online quizzes contribute 40% using the best four marks, two online experiments contribute 10%, and the final exam contributes 50%.
What are the final-exam conditions?
The available wording is: Online, closed book, AI invigilated, and 120 min. The review permits blank papers, a pen and a non-programmable calculator.
Is there a hurdle?
A hurdle is not stated — confirm in the subject outline. A 50% exam weight does not by itself establish a separate pass requirement.
When is the final exam?
No examination date is established in the available materials. Confirm the current subject outline and official examination information.
How do I find a pure Nash equilibrium?
Mark every player’s best responses while holding opponents fixed. A pure profile is Nash exactly when all chosen actions are mutually best responses.
Whose payoff do I equate in a mixed equilibrium?
Equate the opponent’s supported pure-action payoffs to solve your probability, then reverse roles.
Why must an SPE include off-path actions?
An earlier deviation is evaluated using what would happen afterward. Complete contingent strategies make those continuation values and threat credibility checkable.
How is Nature different from a player who mixes?
Nature uses fixed exogenous probabilities and has no preference or best response. A player chooses a distribution strategically to affect incentives.
Why does infinite repetition differ from a long finite game?
A known finite endpoint creates a final stage with no later punishment and can unravel backward. An infinite horizon has no known final stage and can give future punishment enough value.
Are the worked answers official solutions?
No. Every worked answer and extra practice item is AskSia-authored learning material, independently derived from the stated game and not an official answer or marking scheme.
How to study for the exam
Study by algorithm and variation. For normal-form questions, label payoff order, scan strict dominance, mark complete best-response sets, list pure Nash profiles and test plausible mixed supports. For dynamic questions, map information sets, count subgames, write complete strategies, solve the final strategic object and carry continuation values backward. Maintain a threshold ledger recording the original payoff comparison, exact solution, action below, action at equality and action above. Re-derive the two practice-final mixed vectors from their matrices until probability ownership is automatic. Rebuild bargaining from the terminal default rather than memorising the final polynomial. Rebuild repeated-game cutoffs from cooperation, temptation and punishment values rather than memorising one-half. Practise in short closed-book sets that alternate a matrix, a tree, an expectation threshold, bargaining and a trigger inequality. Finish every answer with an independent check: probabilities sum to one, supported payoffs tie, an equilibrium resists unilateral deviation, a threshold reproduces equality, and a strategy profile covers off-path information sets. Confirm all operational requirements in the current subject outline.
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