ECON20005 Chap.7 Continuous Strategies and Reaction Functions
Continuous Strategies and Reaction Functions
Define Continuous Strategy
The course material gives this chapter a concrete anchor: The lecture moves from discrete simultaneous games to continuous strategies and reaction-function methods.
That Continuous Strategy anchor controls how Reaction Function is explained and how Cournot Equilibrium is tested in changed practice.
Continuous Strategies and Reaction Functions is a quantitative decision problem built from Continuous Strategy, Reaction Function and Cournot Equilibrium.
The aim is to derive and intersect reaction functions in a continuous-action game; a numerical result earns meaning only when the variables, units, assumptions and comparison are all explicit.
Begin with Continuous Strategy: 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 Continuous Strategies and Reaction Functions formula checkpoint to Continuous Strategy before calculation begins.
Next connect Reaction Function to the calculation. Show the Reaction Function transformation line by line, preserve units and signs, and make any denominator or baseline visible.
A Reaction Function calculator output is not a method; the reader must be able to reconstruct why that operation answers the question.
Use Cournot Equilibrium to interpret or stress-test the result. Ask whether the Cournot Equilibrium 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 derive and intersect reaction functions in a continuous-action game, separate inputs supplied by the problem from quantities you derive.
Then report the Cournot Equilibrium result in the language of the course and attach the relevant uncertainty, limitation or decision consequence.
Formula checkpoint: Continuous Strategy
A firms reaction function selects the profit-maximising quantity for each quantity chosen by its rival.
Trace Reaction Function
Build a representation check before solving.
Put Continuous Strategy, Reaction Function and Cournot Equilibrium 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 Continuous Strategy 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 Reaction Function, hold the remaining assumptions fixed and recompute only the affected steps. Explain whether the movement in Cournot Equilibrium matches the mechanism.
This Reaction Function sensitivity shows which assumption controls the conclusion and prevents a single scenario from being presented as universal.
Use a three-column Continuous Strategy error log for ECON20005: translation error, calculation error and interpretation error.
Record the exact line where the Reaction Function solution first diverged, rewrite that line, and check it with a limiting case or an independent calculation.
Correcting the first failed Reaction Function 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 Reaction Function, and use Cournot Equilibrium to test the result.
The final sentence about Cournot Equilibrium should answer the question actually asked rather than merely repeat the topic.
The controlling limit is specific: An intersection is meaningful only when it lies in the feasible strategy set and follows from the stated payoff functions.
Keep that Cournot Equilibrium 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 Continuous Strategy, Reaction Function and Cournot Equilibrium without notes, explain their relationship aloud, then complete a changed version of the application: derive and intersect reaction functions in a continuous-action game.
Record the first failed Reaction Function reasoning move and repair it before attempting another case.
What this chapter covers
- 01
Continuous Strategy
- 02
Reaction Function
- 03
Cournot Equilibrium
- 04
Applying Continuous Strategy
- 05
Limits of Reaction Function and Cournot Equilibrium
Continuous Strategies and Reaction Functions: resolve the changed evidence
- 3Fix the case-specific meaning and evidential scale of Continuous Strategy.
- 3Show the operation or inferential link carried by Reaction Function.
- 3Use Cournot Equilibrium to test the strongest plausible alternative.
- 2Report the answer within this limit: An intersection is meaningful only when it lies in the feasible strategy set and follows from the stated payoff functions.
Key terms
- Continuous Strategy
- A strategy selected from a range of possible numerical values rather than from a short discrete list. Use this definition when the task is to derive and intersect reaction functions in a continuous-action game.
- Reaction Function
- A mapping from rivals choices to the players payoff-maximising continuous action. Use this definition when the task is to derive and intersect reaction functions in a continuous-action game.
- Cournot Equilibrium
- A quantity-setting equilibrium in which each firms output is a best response to the outputs of its rivals. Use this definition when the task is to derive and intersect reaction functions in a continuous-action game.
Continuous Strategies and Reaction Functions FAQ
Which inputs and assumptions control the attempt to derive and intersect reaction functions in a continuous-action game?
Derive and intersect reaction functions in a continuous-action game. The lecture moves from discrete simultaneous games to continuous strategies and reaction-function methods. A strategy selected from a range of possible numerical values rather than from a short discrete list.
Is An intersection meaningful only when it lies in the feasible strategy set and follows from the stated payoff functions?
An intersection is meaningful only when it lies in the feasible strategy set and follows from the stated payoff functions. A mapping from rivals choices to the players payoff-maximising continuous action.
Which conclusion should be retested after increasing one firms marginal cost and derive how both equilibrium quantities adjust?
The response first fixes Continuous Strategy at the scale stated in the scenario and excludes evidence that belongs to a different object. It then traces Reaction Function through the relevant evidence rather than assuming the connection. The comparison supplied by Cournot Equilibrium determines whether the initial position remains, narrows or reverses.
The final claim stays conditional on this boundary: An intersection is meaningful only when it lies in the feasible strategy set and follows from the stated payoff functions.
Exam move
Reconstruct the relationship among Continuous Strategy, Reaction Function and Cournot Equilibrium; complete the chapter application without notes; then test the result against this limit: An intersection is meaningful only when it lies in the feasible strategy set and follows from the stated payoff functions..
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