Oligopoly and strategic interaction

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1. What you will learn

Analyze oligopoly and strategic interaction using explicit assumptions, calculated results and a stated limit of the model.

2. Starting point

A firm can have market power without being the only seller. Profit depends on revenue and cost. When another firm's actions affect those outcomes, choosing an action requires considering the other firm's possible response, not merely a fixed market price.

3. Terms and units

4. Interdependence changes the decision problem

In an oligopoly, a few major sellers account for much of a defined market. Each can expect its pricing, output or product decisions to affect rivals, and those rivals' responses can affect its own results. This strategic interdependence distinguishes the setting from the simplest competitive price-taking model. It also differs from a monopoly, which has no rival seller within the defined market to respond directly.

An oligopoly can arise from entry barriers, scale economies, scarce resources or other conditions limiting the number of effective competitors. The number of firms alone does not determine a unique price or quantity. Outcomes depend on how firms interact: whether they choose prices or quantities, whether choices are simultaneous, how products differ, what firms know and whether interaction repeats. A model must specify those rules before its predictions become determinate.

Game theory represents such interaction through players, feasible actions, payoffs and timing. A two-by-two payoff table is a compact model of two players each choosing between two actions. Each cell contains a pair of payoffs, conventionally row player's payoff first and column player's payoff second. The convention must be stated because swapping the entries can reverse a best-response calculation. The numbers may be profits in dollars, but a different stated objective would require a different interpretation.

The actions' labels do not by themselves establish which is best. Calling one action cooperative or aggressive can suggest a story, but the strategic solution comes from the payoffs and rules. We use C and D as neutral codes and explicitly translate them where needed. A learner is asked to reconstruct each player's incentives within the supplied game, not to choose the behavior that sounds socially admirable.

Term	What it means
Oligopoly	A market with a small number of strategically interdependent major sellers.
Strategy	A specified action or contingent plan available to a player.
Payoff	The outcome a player evaluates under the game's stated objective, such as profit.
Best response	An action giving the player the highest payoff against a specified action of the other player.
Dominant strategy	An action that is best against every action available to the other player, with strictness determined by the comparisons.
Nash equilibrium	An action combination where no player can gain by changing only that player's own action.
Collusion	Coordination among firms intended to influence market outcomes, whose feasibility and legality are separate issues.

Another way: Find best responses one opponent action at a time

Consider two firms choosing simultaneously between C and D. If both choose C, each earns four dollars. If the row firm chooses D while the column firm chooses C, payoffs are six for row and zero for column. If row chooses C and column D, the payoffs reverse to zero and six. If both choose D, each earns two. The first step is to hold one player's action fixed and compare only the other player's available payoffs.

Against column C, row compares four from C with six from D and prefers D. Against column D, row compares zero from C with two from D and again prefers D. D is therefore a strictly dominant strategy for row: it gives a strictly higher payoff in each comparison. The conclusion does not come from selecting the largest number anywhere in the table. It comes from a separate within-column comparison for each possible rival action.

For the column player, hold the row action fixed and compare the second entries across columns. Against row C, column obtains four from C or six from D, so chooses D. Against row D, column obtains zero from C or two from D, so again chooses D. Symmetry makes the result match row's, but the calculation should still use column's own payoffs. A nonsymmetric game may give the players different best responses.

A dominant strategy need not exist. If an action is best against one rival choice but another action is best against the other, the player's preferred action depends on expectations or the equilibrium analysis. Absence of a dominant strategy does not imply that the game has no Nash equilibrium. Likewise, a weakly dominant strategy can tie in some comparisons while doing better in others. Our numerical examples use strict comparisons unless a tie rule is explicitly supplied.

Another way: Check mutual stability, not just a large total

The outcome DD is a Nash equilibrium in the example because each player's D is a best response to the other's D. Starting there, if row alone changes to C, row's payoff falls from two to zero. If column alone changes to C, column's payoff also falls from two to zero. Neither has an incentive to make a unilateral deviation. That is the equilibrium test.

The outcome CC gives a higher combined payoff: eight dollars rather than four. It is not Nash because either player can raise its own payoff from four to six by changing alone to D while the other remains at C. A jointly preferable outcome need not be stable under individual incentives. This conflict between collective and unilateral interests is the central feature of the prisoner's-dilemma structure represented by the table.

Nash equilibrium does not mean that every player receives the largest payoff it could ever receive, that the total is maximized or that the outcome is fair. It means no player can improve by changing only its own action while the others' actions remain fixed. That counterfactual is precise. A comparison that changes both players' actions simultaneously is not a test of a unilateral deviation, although it can reveal a better joint outcome.

Some games have multiple pure-strategy Nash equilibria, and some have none. To search a finite table, mark each player's best responses and locate cells containing both. If no cell qualifies, a pure-strategy answer is absent; a mixed-strategy analysis may be relevant, but it requires additional concepts beyond our introductory constructed tasks. Do not force a single cell merely because a question presents a small table. The existence and uniqueness of an equilibrium must come from the payoff comparisons.

Another way: Collusion, repeated interaction and limits of the table

Firms may try to coordinate on a jointly profitable outcome, such as restricting output or avoiding price cuts. The one-shot example shows why maintaining that arrangement can be difficult: each firm can gain by deviating while its rival cooperates. An agreement's announced existence does not remove the incentive. Effective enforcement, monitoring or a different game structure would be needed to change the comparison.

Repeated interaction can alter incentives because a current deviation may affect future behavior. If a firm expects rivals to respond to a deviation with lower future cooperation, the short-run gain must be compared with the discounted future loss. Whether cooperation can be sustained depends on patience, monitoring, the credibility of responses and the precise strategies available. Repetition does not automatically guarantee collusion, and a one-shot payoff table alone does not determine the repeated-game outcome.

Sequential interaction also differs from simultaneous choice. If one firm moves first and another observes before responding, the first firm can anticipate that response. A game tree and backward reasoning may be appropriate. The simultaneous table assumes neither player conditions its current action on observing the other's current move. Reinterpreting it as a sequential game without changing the solution method would answer a different question.

The payoffs may omit costs or benefits to consumers and other parties. Even if firms maximize their combined profit, that is not necessarily the total-surplus maximum for the market. Higher producer profit can accompany lower consumer surplus or restricted beneficial trade. A welfare analysis needs demand, costs and any external effects, not just the two firms' profit table. Keep the game's private objectives separate from a public evaluation criterion.

Legal questions about coordination are also distinct from solving the model. The classroom game does not advise firms to communicate, coordinate prices or evade rules. It explains incentives under an invented set of actions. Actual competition law and institutional details vary and would require separate authoritative analysis. Our graded response is limited to best responses, equilibrium codes and payoff calculations from the supplied table.

An effective written explanation identifies the fixed rival action in each comparison, names the player's own payoff entries and checks any proposed equilibrium for unilateral deviations. It then distinguishes equilibrium from joint payoff and states the timing assumption. This sequence gives the learner a reusable method without pretending that every oligopoly behaves exactly like the same two-action game.

Another way: Keep units and objectives consistent

A payoff pair records two separate evaluations, so adding them is appropriate only when the question explicitly asks for a combined amount on a common scale. Our firms profits are measured in the same dollars and period, making that sum an intelligible accounting total. If the entries instead represented different personal utility scales, their numerical sum would not automatically be a meaningful measure of social welfare.

5. Two fictional kiosks choose their service plan

Two invented kiosks choose C or D for a one-day service plan without seeing the other's current choice. The stipulated profit table gives each four dollars under CC and two under DD. A kiosk choosing D against a rival's C earns six, while the rival earns zero. The exercise does not require interpreting the action labels as morally good or bad; their economic consequences are contained in the table.

The row kiosk first holds the rival at C and compares four with six, choosing D. It then holds the rival at D and compares zero with two, again choosing D. The column kiosk has the same comparisons using its own payoff entries. DD is the unique pure-strategy Nash equilibrium and generates a combined payoff of four. CC would generate eight, but either kiosk could improve its own payoff by deviating alone. The higher combined amount therefore does not make CC stable in this one-shot model.

Suppose someone proposes solving the problem by choosing the cell containing a six. That overlooks the other player's incentive and fails to identify a mutual best response. Someone else proposes choosing CC because its sum is largest. That answers a joint-optimization question, not the stipulated independent-choice game. Both mistakes become visible when each player's comparison is written separately.

If the kiosks instead interact daily and future consequences are added, the model has changed. A new analysis would need the repeated-game rules and how future payoffs are valued. The original answer remains correct for the one-day simultaneous game, but it cannot settle the repeated case. The application demonstrates how a small payoff table supports a precise conclusion while leaving broader market and welfare questions open.

6. Check the tempting shortcut

The largest cell entry and the largest combined payoff need not identify Nash equilibrium. Hold the rival's action fixed and compare the player's own payoffs. Nash concerns unilateral deviations; repeated or sequential interaction requires rules beyond a one-shot simultaneous table.

7. In the fictional Alder model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(5,5), CD=(1,7), DC=(7,1), DD=(3,3). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

8. In the fictional Birch model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(6,6), CD=(2,8), DC=(8,2), DD=(4,4). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

9. In the fictional Cedar model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(7,7), CD=(3,9), DC=(9,3), DD=(5,5). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

10. In the fictional Dune model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(8,8), CD=(4,10), DC=(10,4), DD=(6,6). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

11. Guided practice

In the fictional Elm model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(9,9), CD=(5,11), DC=(11,5), DD=(7,7). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

12. Guided practice

In the fictional Dune model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(8,8), CD=(4,10), DC=(10,4), DD=(6,6). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

13. Guided practice

In the fictional Fern model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(10,10), CD=(6,12), DC=(12,6), DD=(8,8). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

14. Practice

In the fictional Grove model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(11,11), CD=(7,13), DC=(13,7), DD=(9,9). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

15. Practice

In the fictional Harbor model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(12,12), CD=(8,14), DC=(14,8), DD=(10,10). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

16. Somewhere new

Two kiosks simultaneously select their one-day service plans. A coordinator recommends the cell with the highest combined profit, but the kiosks each optimize only their own profit and cannot make a binding agreement. Audit unilateral incentives before reporting the equilibrium total. In the fictional Island model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(13,13), CD=(9,15), DC=(15,9), DD=(11,11). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

17. Lesson test

Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.

18. Test question

In the fictional Juniper model, two firms choose C or D simultaneously once. Their payoff pairs (row firm, column firm), in dollars, are CC=(14,14), CD=(10,16), DC=(16,10), DD=(12,12). Each seeks its own payoff. Encode C=0 and D=1. Report the row firm's best response to column C, its best response to column D, and the sum of both firms' payoffs at the Nash equilibrium. No binding agreement is possible.

19. What you can do now

Reconstruct the model without the worked example. Explain each requested measure's units and identify an assumption that the conclusion depends on.

Working for the steps left to you

	Calculated value
Response to C (0 or 1)
Response to D (0 or 1)
Equilibrium payoff sum

	Calculated value
Response to C (0 or 1)
Response to D (0 or 1)
Equilibrium payoff sum

	Calculated value
Response to C (0 or 1)
Response to D (0 or 1)
Equilibrium payoff sum

	Calculated value
Response to C (0 or 1)
Response to D (0 or 1)
Equilibrium payoff sum