ECON20005 Chap.3 Sequential Games and Game Trees
Sequential Games and Game Trees
Define Game Tree
The course material gives this chapter a concrete anchor: The lecture introduces sequential games and uses game trees to connect order of moves with complete payoff consequences.
That Game Tree anchor controls how Decision Node is explained and how Terminal Payoff is tested in changed practice.
Sequential Games and Game Trees is a quantitative decision problem built from Game Tree, Decision Node and Terminal Payoff.
The aim is to translate a sequential scenario into nodes, branches and payoffs; a numerical result earns meaning only when the variables, units, assumptions and comparison are all explicit.
Begin with Game Tree: state what quantity it represents, the scale on which it is measured and the condition under which it changes.
Then map every symbol in the Sequential Games and Game Trees formula checkpoint to Game Tree before calculation begins.
Next connect Decision Node to the calculation. Show the Decision Node transformation line by line, preserve units and signs, and make any denominator or baseline visible.
A Decision Node calculator output is not a method; the reader must be able to reconstruct why that operation answers the question.
Formula checkpoint: Game Tree
At a terminal history h, each players continuation value equals the payoff assigned to the resulting outcome z.
Trace Decision Node
Use Terminal Payoff to interpret or stress-test the result.
Ask whether the Terminal Payoff magnitude is plausible, whether a boundary case behaves as expected and which conclusion would reverse if an assumption changed. This is where computation becomes analysis rather than arithmetic.
When the task is to translate a sequential scenario into nodes, branches and payoffs, separate inputs supplied by the problem from quantities you derive.
Then report the Terminal Payoff result in the language of the course and attach the relevant uncertainty, limitation or decision consequence.
Build a representation check before solving. Put Game Tree, Decision Node and Terminal Payoff into a small symbol-and-units table, mark which values are observed and which are calculated, and predict the direction of the result before doing arithmetic.
A sign, scale or unit mismatch in Game Tree then becomes visible at setup instead of being hidden inside a polished final number.
Run one sensitivity test after the baseline answer. Change the input most closely connected to Decision Node, hold the remaining assumptions fixed and recompute only the affected steps. Explain whether the movement in Terminal Payoff matches the mechanism.
This Decision Node sensitivity shows which assumption controls the conclusion and prevents a single scenario from being presented as universal.
Test with Terminal Payoff
Use a three-column Game Tree error log for ECON20005: translation error, calculation error and interpretation error.
Record the exact line where the Decision Node solution first diverged, rewrite that line, and check it with a limiting case or an independent calculation.
Correcting the first failed Decision Node move is more useful than copying the complete solution again.
A complete response should make the task visible before the detail: identify what must be decided, define the relevant terms, connect the evidence to Decision Node, and use Terminal Payoff to test the result.
The final sentence about Terminal Payoff should answer the question actually asked rather than merely repeat the topic.
The controlling limit is specific: Every complete path needs a payoff for each player, and a missing feasible branch changes the game being solved.
Keep that Terminal Payoff limit beside the worked example, because it separates a careful ECON20005 answer from one that sounds confident but claims more than the task or evidence supports.
For revision, retrieve Game Tree, Decision Node and Terminal Payoff without notes, explain their relationship aloud, then complete a changed version of the application: translate a sequential scenario into nodes, branches and payoffs.
Record the first failed Decision Node reasoning move and repair it before attempting another case.
What this chapter covers
- 01
Game Tree
- 02
Decision Node
- 03
Terminal Payoff
- 04
Applying Game Tree
- 05
Limits of Decision Node and Terminal Payoff
Sequential Games and Game Trees: resolve the changed evidence
- 4Fix the case-specific meaning and evidential scale of Game Tree.
- 3Show the operation or inferential link carried by Decision Node.
- 3Use Terminal Payoff to test the strongest plausible alternative.
- 3Report the answer within this limit: Every complete path needs a payoff for each player, and a missing feasible branch changes the game being solved.
Key terms
- Game Tree
- A branching representation of moves, information and resulting outcomes in a sequential game. Use this definition when the task is to translate a sequential scenario into nodes, branches and payoffs.
- Decision Node
- A point at which a specified player chooses among the available actions. Use this definition when the task is to translate a sequential scenario into nodes, branches and payoffs.
- Terminal Payoff
- The payoff vector attached to a completed path after all relevant moves have occurred. Use this definition when the task is to translate a sequential scenario into nodes, branches and payoffs.
Sequential Games and Game Trees FAQ
What must survive the move required to translate a sequential scenario into nodes, branches and payoffs?
Translate a sequential scenario into nodes, branches and payoffs. The lecture introduces sequential games and uses game trees to connect order of moves with complete payoff consequences.
Which condition in this chapter explains why Every complete path needs a payoff for each player, and a missing feasible branch changes the game being solved?
Every complete path needs a payoff for each player, and a missing feasible branch changes the game being solved. A point at which a specified player chooses among the available actions.
If a student were to insert a new response at the second decision node, how should they redraw every affected terminal payoff?
The response first fixes Game Tree at the scale stated in the scenario and excludes evidence that belongs to a different object. It then traces Decision Node through the relevant evidence rather than assuming the connection. The comparison supplied by Terminal Payoff determines whether the initial position remains, narrows or reverses.
The final claim stays conditional on this boundary: Every complete path needs a payoff for each player, and a missing feasible branch changes the game being solved.
Exam move
Reconstruct the relationship among Game Tree, Decision Node and Terminal Payoff; complete the chapter application without notes; then test the result against this limit: Every complete path needs a payoff for each player, and a missing feasible branch changes the game being solved..
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