Can individually attractive choices lower both firms’ profits?
Your task: Draw the two-by-two payoff matrix, circle best responses, and explain why the cooperative outcome is not the predicted one-shot equilibrium.
Read counts with their units. A percentage divides a part by its named whole and multiplies by 100. A model assumption is not an observed fact.
Nash equilibrium
A strategy combination where no player gains by changing only their own choice, given the model.
Assumption
A condition accepted for a model or argument; it needs justification before applying the result elsewhere.
01 · TRY
Can individually attractive choices lower both firms’ profits?
Draw the two-by-two payoff matrix, circle best responses, and explain why the cooperative outcome is not the predicted one-shot equilibrium.
Draw the two-by-two payoff matrix, circle best responses, and explain why the cooperative outcome is not the predicted one-shot equilibrium. Use the supplied records and show one intermediate step.
Make a provisional claim
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Inspect evidence and test an explanation
The investigation controls appear when your local evidence is ready.
04 · UNDERSTAND
Connect evidence and mechanism
Inspect strategic interaction and entry
Question and evidence
Can individually attractive choices lower both firms’ profits?
Two fictional firms choose Hold or Cut. Profits (A,B) are (8,8) if both Hold, (10,3) if A Cuts and B Holds, (3,10) if B Cuts and A Holds, and (5,5) if both Cut. Choices are simultaneous and made once.
This packet uses fictional data to isolate a mechanism. It is not an empirical estimate.
Mechanism and worked example
A dominant strategy is best regardless of the other player’s choice. A Nash equilibrium gives neither player a profitable unilateral deviation under the stated choices. Strategic interaction differs from price-taking. With differentiated products and entry, monopolistic competition raises separate questions about short-run profit and long-run entry.
If B Holds, A prefers Cut (10>8); if B Cuts, A prefers Cut (5>3). Symmetry gives Cut/Cut, with (5,5), as the one-shot equilibrium, though Hold/Hold gives larger combined profit.
Complication
A manager predicts both will Hold because total profit is highest there. No binding agreement exists. Repeated interaction, entry, differentiation and competition law are outside the one-shot payoff table; the exercise is not advice to coordinate prices.
Your investigation
Draw the two-by-two payoff matrix, circle best responses, and explain why the cooperative outcome is not the predicted one-shot equilibrium.
Revise your answer to “Can individually attractive choices lower both firms’ profits?” using both source IDs. Separate the checked calculation from a judgment, and identify evidence that could reverse your judgment.
Vocabulary
Nash equilibrium: A strategy combination where no player gains by changing only their own choice, given the model.
Assumption: A condition accepted for a model or argument; it needs justification before applying the result elsewhere.
Independent extension
Independently extend the investigation “Inspect strategic interaction and entry” with a documented real dataset or scholarly source. Preserve definitions, recreate one calculation or evidence table, compare a rival explanation and report why the teaching example cannot establish the real-world conclusion.
Audit conditional choices, ties and stability
Two fictional firms choose simultaneously once. A chooses a row; B chooses a column. Each cell lists (A profit, B profit) in stipulated credits per period. Upper/Lower and Left/Right are abstract alternatives, not instructions to coordinate real prices. Each firm maximizes its own payoff, knows the table, and cannot change the rival's choice. No binding agreement or repetition is modeled.
Predict: mark A's best row in each column and B's best column in each row. Can an outcome maximize combined profit yet allow a profitable unilateral change? Does absence of a dominant strategy imply absence of a stable outcome?
A rows / B columnsB LeftB RightA UpperA Lower
Selected: A Upper / B Left; A=8, B=7, combined profit=15. These sums exclude consumers and external effects; the largest sum is not a social-welfare optimum.
Changed evidence and transfer
In Conditional choices, explain why two outcomes are stable although neither firm has a dominant choice. Then choose the tie case: only A's Lower/Left payoff changes from 3 to 7. Recheck every equilibrium and dominance claim. Finally inspect the no-stable-pure-choice transfer: document a profitable unilateral deviation from each of its four cells before making any equilibrium claim.
Reasoning guide and institutional limits
The first case has A Lower and B Right strictly dominant: Lower/Right gives (4,3), while Upper/Left maximizes combined profit at 15 but allows both unilateral gains. Conditional choices has Upper/Left and Lower/Right equilibria with no dominant strategies. Changing A's Lower/Left payoff to 7 leaves both equilibria and makes Lower weakly, but not strictly, dominant for A. The transfer has no pure equilibrium: from Upper/Left B gains 3; Upper/Right A gains 3; Lower/Left A gains 3; Lower/Right B gains 6.
A joint-profit maximum does not establish a binding agreement, legal permission, enforceability or an actual market prediction. The table contains no consumers, entry response, uncertainty or enforcement institution. Repetition could change incentives but is not analyzed here; do not infer that collaboration is universally stable or socially desirable.
Method reference and original data
OpenStax Microeconomics 3e, section 10.2 supplies introductory context for one-shot strategic interdependence. All matrices and interface material here are original fictional teaching examples; no textbook data or prose is copied. This is an ungraded bounded practice comparison.
Copy the strategic-choice report
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Worked example
If B Holds, A prefers Cut (10>8); if B Cuts, A prefers Cut (5>3). Symmetry gives Cut/Cut, with (5,5), as the one-shot equilibrium, though Hold/Hold gives larger combined profit.
