ECON20005 Chap.4 Backward Induction and Credibility
Backward Induction and Credibility
Define Backward Induction
The course material gives this chapter a concrete anchor: The lecture extends sequential-game analysis through backward induction, credibility and more complex continuations.
That Backward Induction anchor controls how Credible Threat is explained and how Subgame is tested in changed practice.
Backward Induction and Credibility is a quantitative decision problem built from Backward Induction, Credible Threat and Subgame.
The aim is to solve a sequential game from later choices and separate credible from empty threats; a numerical result earns meaning only when the variables, units, assumptions and comparison are all explicit.
Begin with Backward Induction: 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 Backward Induction and Credibility formula checkpoint to Backward Induction before calculation begins.
Next connect Credible Threat to the calculation. Show the Credible Threat transformation line by line, preserve units and signs, and make any denominator or baseline visible.
A Credible Threat calculator output is not a method; the reader must be able to reconstruct why that operation answers the question.
Use Subgame to interpret or stress-test the result. Ask whether the Subgame 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 solve a sequential game from later choices and separate credible from empty threats, separate inputs supplied by the problem from quantities you derive.
Then report the Subgame result in the language of the course and attach the relevant uncertainty, limitation or decision consequence.
Formula checkpoint: Backward Induction
At each reached decision history, the player selects an available action with the highest continuation value.
Trace Credible Threat
Build a representation check before solving.
Put Backward Induction, Credible Threat and Subgame 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 Backward Induction 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 Credible Threat, hold the remaining assumptions fixed and recompute only the affected steps. Explain whether the movement in Subgame matches the mechanism.
This Credible Threat sensitivity shows which assumption controls the conclusion and prevents a single scenario from being presented as universal.
Use a three-column Backward Induction error log for ECON20005: translation error, calculation error and interpretation error.
Record the exact line where the Credible Threat solution first diverged, rewrite that line, and check it with a limiting case or an independent calculation.
Correcting the first failed Credible Threat 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 Credible Threat, and use Subgame to test the result.
The final sentence about Subgame should answer the question actually asked rather than merely repeat the topic.
The controlling limit is specific: A threatened action is not credible merely because it changes an earlier players choice; it must be optimal in the continuation game.
Keep that Subgame 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 Backward Induction, Credible Threat and Subgame without notes, explain their relationship aloud, then complete a changed version of the application: solve a sequential game from later choices and separate credible from empty threats.
Record the first failed Credible Threat reasoning move and repair it before attempting another case.
What this chapter covers
- 01
Backward Induction
- 02
Credible Threat
- 03
Subgame
- 04
Applying Backward Induction
- 05
Limits of Credible Threat and Subgame
Backward Induction and Credibility: resolve the changed evidence
- 4Fix the case-specific meaning and evidential scale of Backward Induction.
- 4Show the operation or inferential link carried by Credible Threat.
- 4Use Subgame to test the strongest plausible alternative.
- 3Report the answer within this limit: A threatened action is not credible merely because it changes an earlier players choice; it must be optimal in the continuation game.
Key terms
- Backward Induction
- A solution method that begins at later decision nodes and replaces each continuation with the choosing players preferred feasible action. Use this definition when the task is to solve a sequential game from later choices and separate credible from empty threats.
- Credible Threat
- A threatened action that remains optimal for the player if the decision point is actually reached. Use this definition when the task is to solve a sequential game from later choices and separate credible from empty threats.
- Subgame
- A part of a sequential game beginning at a valid decision node and containing all of its successors without cutting an information set. Use this definition when the task is to solve a sequential game from later choices and separate credible from empty threats.
Backward Induction and Credibility FAQ
Which inputs and assumptions control the attempt to solve a sequential game from later choices and separate credible from empty threats?
Solve a sequential game from later choices and separate credible from empty threats. The lecture extends sequential-game analysis through backward induction, credibility and more complex continuations.
Must A threatened action is not credible merely because it changes an earlier players choice; it be optimal in the continuation game?
A threatened action is not credible merely because it changes an earlier players choice; it must be optimal in the continuation game. A threatened action that remains optimal for the player if the decision point is actually reached.
If a student were to reverse the later players payoff ranking, how should they recompute the earlier players best move?
The response first fixes Backward Induction at the scale stated in the scenario and excludes evidence that belongs to a different object. It then traces Credible Threat through the relevant evidence rather than assuming the connection. The comparison supplied by Subgame determines whether the initial position remains, narrows or reverses.
The final claim stays conditional on this boundary: A threatened action is not credible merely because it changes an earlier players choice; it must be optimal in the continuation game.
Exam move
Reconstruct the relationship among Backward Induction, Credible Threat and Subgame; complete the chapter application without notes; then test the result against this limit: A threatened action is not credible merely because it changes an earlier players choice; it must be optimal in the continuation game..
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