23506 Strategic Decision Making and Game Theory
The Complete Exam Bible · Spring 202623506 Overview
- University of Technology Sydney
- Spring 2026
- 13 chapters
- Economics
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.
- Assessed by Online quizzes 40% · Online experiments 10% · Final exam 50%
- Key terms Best response, Strict dominance, Nash equilibrium, Mixed strategy
- How to prepare Study by algorithm and variation.
- Most asked What are the assessment weights?
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.
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.
Game Theory Foundations: Normal-Form Games, Payoff Matrices and the Classic 2×2 Games
Players, strategies, profiles, payoff order, strategic interaction and the canonical coordination, conflict and cyclic gamesGame theory studies situations in which each decision maker’s payoff depends on a profile of choices, not on one choice in isolation. A normal-form game states the players, each player’s strategy set and a payoff for every strategy profile.
- Players, strategies, profiles and ordered payoffs
- Matrix coordinate and unilateral-deviation discipline
- Prisoner’s Dilemma and collective loss
- Battle of the Sexes and coordination selection
- Stag Hunt, payoff dominance and security
- Chicken, response cycles, auctions and demand
Best Response, Strict vs Weak Dominance, and Iterated Elimination
Response correspondences, strict and weak comparisons, deletion ledgers and second-price-auction logicA best response is any feasible action that maximises a player’s payoff against fixed opposing strategies. It can be unique or set-valued when several actions tie at the maximum.
- Best-response correspondences and ties
- Strict dominance and universal comparison
- Weak dominance and equality
- Iterated deletion in reduced games
- Order sensitivity and mixed dominance
- Truthful bidding in a second-price auction
Nash Equilibrium in Matrix Games: The Check Method, Focal Points, Payoff vs Risk Dominance
Mutual best responses, equilibrium patterns, focal selection, payoff dominance and risk dominanceA pure-strategy Nash equilibrium is a profile in which every player’s chosen action is a best response to the others.
- Pure Nash equilibrium as mutual best response
- Two-colour matrix check method
- Coordination, anti-coordination and cycles
- Focal points and selection evidence
- Payoff dominance versus stability
- Risk dominance and self-fulfilling beliefs
Nash Equilibrium Applications: Cournot, Bertrand, Entry and the Demand Game
Quantity and price competition, integer entry conditions, resource claims and guess-and-verify equilibriumApplied Nash problems often hide a familiar mutual-best-response check inside a richer strategy space. In the discrete Cournot model, firms simultaneously choose quantities from 0,1,2,3. Inverse demand is p=10−xA−xB and profit is (10−xA−xB)xi−4.5xi.
- Discrete Cournot profit and reaction schedules
- Cournot equilibrium (2,2) and profit verification
- Demand-game resource boundary
- Integer entry and adjacent-firm checks
- Bertrand prices and undercutting
- Controlled comparison of quantity, price and timing
Mixed-Strategy Nash Equilibrium: Expected Payoffs and the Indifference Condition
Probability ownership, support selection, best-response crossings and complete equilibrium setsA mixed strategy is a probability distribution over pure strategies chosen before the realised action. It can make a player strategically unpredictable when no pure profile is stable, and it can coexist with pure equilibria in coordination games.
- Probability distributions and support
- Expected payoff and probability complements
- Cross-player indifference equations
- Best-response crossings
- Mixed equilibrium in penalty and coordination games
- Three-action support checks and interpretations
Mixed-Strategy Applications: Tennis Serve, Entry and Detective Games
Strategic unpredictability, congestion, targeting, auditing and symbolic comparative staticsMixed strategies become concrete when predictability itself is costly.
- Mixed entry and congestion
- Outcome probabilities and expected entrants
- First- and second-serve tennis
- Asymmetric serve probabilities
- Detective target values
- Auditing, deterrence and comparative statics
Extensive-Form Games, Game Trees and Subgame Perfect Equilibrium
Information sets, proper subgames, complete contingent strategies, credibility and backward inductionAn extensive-form tree records chronological decisions, available actions, information and terminal payoffs. Each decision node belongs to a player; each branch carries an action; each terminal node keeps one declared payoff order.
- Nodes, branches and terminal payoff order
- Information sets and observation
- Strategies as complete contingency plans
- Normal-form conversion
- Proper subgames and nesting
- Credibility, backward induction and SPE
SPE Applications: Stackelberg, First-Mover Advantage and Nature's Move
Follower reaction plans, leadership commitment, chance nodes and probability-region equilibriaStackelberg quantity competition uses the Cournot demand and cost primitives but changes timing. Firm A commits first; Firm B observes and responds. The follower’s strategy is not one output but a response after every possible leader quantity.
- Simultaneous continuations inside subgames
- Stackelberg timing and commitment
- Follower response tuple (3,2,2,1)
- Leader output 3 and path (3,1)
- Nature, expectation and insurance
- Oil-well thresholds 1/5 and 2/7
Limits of SPE: Forward Induction, Trust Game, Chain-Store Paradox, Centipede
Equilibrium selection, behavioural prediction, reputation, finite-horizon induction and efficiency tensionSubgame perfection gives disciplined continuation play but can leave selection or prediction questions open. In the outside-option Battle of the Sexes, Study gives (2,2), while Date leads to a subgame with equilibria (S,S) and (F,F).
- Multiple SPEs with an outside option
- Forward induction through dominance
- Trust game and selfish-payoff SPE
- Chain-store non-credible deterrence
- Reputation through type uncertainty
- Four- and 100-period centipede induction
Sequential Bargaining: Time Discounting, Outside Options and Bargaining Power
Alternating offers, acceptance thresholds, terminal defaults, patience and immediate agreementSequential bargaining adds a protocol to a division problem: who proposes, who responds, what rejection leads to and how delay changes value. With discount factor δ in (0,1), a payoff z received k periods after the evaluation date is worth δ^kz.
- Bargaining protocols and reservation values
- Exponential discounting and delay count
- Period-2 acceptance x2≥δy
- Initial claim 1−δ+δ²y
- Default and patience as bargaining power
- Pie of eight with default (2,2)
Repeated Prisoner's Dilemma: Trigger Strategies, Finite vs Infinite Horizon, Folk Theorem
Histories, finite unraveling, geometric continuation values, grim-trigger thresholds and cooperative possibilityRepeated interaction expands strategy from a current action to a rule after every public history. The lecture Prisoner’s Dilemma has payoffs (2,2) under mutual cooperation, temptation 3 against a cooperator and punishment 1 under mutual defection.
- Public histories and repeated-game strategies
- Unconditional and grim-trigger plans
- Known finite-horizon unraveling
- Infinite geometric continuation values
- Grim-trigger cutoff δ≥1/2
- Problem-set cutoff δ≥2/9 and folk intuition
The Maths Toolkit: Interval vs Set Notation, Expected Value and Discounted Infinite Sums
Domains, functions, complements, argmax, expected payoff, inequalities and geometric-series disciplineMathematics in 23506 records feasible choices, information and incentives. Intervals such as [0,100] include both boundaries, while (0,1) excludes them. Parameter solutions should partition the entire feasible domain without gaps or overlap.
- Intervals, sets and equality points
- Functions and contingent strategies
- Expected value before unresolved states
- Mixed expected payoff and probability ownership
- Inequalities, argmax and piecewise responses
- Finite and infinite discounted sums
Final Exam Playbook: Question Structure, 120-Minute Pacing and the Practice Exam Walkthrough
Question triage, true-or-false proofs, matrix re-solutions, demand-game review and final verificationThe 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.
- Final conditions and flexible pacing
- Question-family triage
- True-or-false proof method
- Practice matrices 2a and 2c
- Practice matrices 2b and 2d re-solutions
- Demand-game, tree and calculation audits
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.
Worked example · free
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.
Questions students ask in each 23506 chapter
- What is the first number in a payoff pair?
- It is the payoff of the first player in the declared ordering, normally Row in this guide. Always check the matrix label. Chapter 01 · Game Theory Foundations: Normal-Form Games, Payoff Matrices and the Classic 2×2 Games
- Can a player have two best responses?
- Yes. Keep both when they tie at the highest payoff. Chapter 02 · Best Response, Strict vs Weak Dominance, and Iterated Elimination
- Is every highest-total-payoff cell Nash?
- No. Each player must resist a unilateral deviation; total payoff is not the criterion. Chapter 03 · Nash Equilibrium in Matrix Games: The Check Method, Focal Points, Payoff vs Risk Dominance
- Why is (2,2) Cournot Nash?
- Each firm earns more at quantity 2 than at 0,1 or 3 when the rival supplies 2. Chapter 04 · Nash Equilibrium Applications: Cournot, Bertrand, Entry and the Demand Game
- Why must supported actions tie?
- If one paid less, shifting its probability to the higher action would improve payoff. Chapter 05 · Mixed-Strategy Nash Equilibrium: Expected Payoffs and the Indifference Condition
- Why is entry probability 1/3?
- It makes expected entry payoff 2−6p equal the zero payoff from staying out. Chapter 06 · Mixed-Strategy Applications: Tennis Serve, Entry and Detective Games
- Does every decision node start a subgame?
- No. The node must be a singleton information set and its continuation cannot cut another information set. Chapter 07 · Extensive-Form Games, Game Trees and Subgame Perfect Equilibrium
- Why is (3,1) incomplete?
- It is only the path. The follower must also specify responses after leader deviations. Chapter 08 · SPE Applications: Stackelberg, First-Mover Advantage and Nature's Move
- Does SPE choose one outside-option outcome?
- No. Two subgame equilibria generate two continuation values and two SPEs. Chapter 09 · Limits of SPE: Forward Induction, Trust Game, Chain-Store Paradox, Centipede
- What does δ measure?
- Patience: a payoff one period later is worth δ times its amount at the current date. Chapter 10 · Sequential Bargaining: Time Discounting, Outside Options and Bargaining Power
- What is a repeated-game strategy?
- A mapping from every relevant history to a current action. Chapter 11 · Repeated Prisoner's Dilemma: Trigger Strategies, Finite vs Infinite Horizon, Folk Theorem
- What does [a,b] mean?
- Both a and b are included; parentheses exclude the corresponding endpoint. Chapter 12 · The Maths Toolkit: Interval vs Set Notation, Expected Value and Discounted Infinite Sums
- How long is the final?
- The available wording states 120 minutes. Chapter 13 · Final Exam Playbook: Question Structure, 120-Minute Pacing and the Practice Exam Walkthrough
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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