MGEA02H3 Chap.9 Oligopoly and Game Theory
Oligopoly and Game Theory
Strategic interaction
In an oligopoly a few firms each depend on the others’ choices. The course models a duopoly with a payoff matrix: each cell gives each firm’s profit at the combined output, assuming each firm takes its rival’s output as given.
The joint-profit-maximising cell and the stable cell, the Nash equilibrium, are marked separately, and the prisoners’ dilemma explains why they differ.
Welfare across structures
A firm that raises output from the joint-profit cell gains revenue while the industry loses it, so collusion is unstable.
Recent finals also posed the duopoly algebraically, with Nash output (a − c)/3b per firm and cartel output (a − c)/2b in total.
The gain to society ranks competition first, then non-collusive oligopoly, then cartel.
What the answer keys reward
Matrix keys compute each cell from the market price at the combined output, mark each firm’s incentive with arrows, and outline the cell no arrow leaves as the stable outcome, with the joint-profit cell marked separately.
Explanations contrast the firm’s gain from extra output with the industry’s loss.
Welfare items compute consumer surplus and total profit for each regime and rank them, with competition first and collusion last.
How this topic connects to later chapters
The prisoners’ dilemma reappears in chapter 10, where neighbours each choose not to pay for a shared benefit or to keep a harmful practice, and the dominant-strategy logic explains why public goods and pollution control need coordination or government action.
The welfare ranking of this chapter also completes the comparison of market structures that began with perfect competition.
What this chapter covers
- 01
Payoff matrices for a duopoly
- 02
Dominant strategies and Nash equilibrium
- 03
Joint-profit maximisation and cartels
- 04
Why collusion breaks down
- 05
Algebraic duopoly with linear demand
- 06
Ranking welfare across market structures
Worked example · free
Filling a duopoly matrix and ranking welfare
- 2Both at 12: P = $52 and each earns $576.
- 216 against 12: P = $44, earning $640 and $480.
- 2Both at 16: P = $36 and each earns $512.
- 216 is dominant, so (16, 16) is stable; (12, 12) maximises joint profit.
Key terms
- Nash Equilibrium
- A Nash equilibrium is a set of choices in which no player can gain by changing only its own choice.
- Dominant Strategy
- A dominant strategy is a choice that gives a player the higher payoff whatever the other player does.
- Prisoners' Dilemma
- The prisoners' dilemma is a game in which each player’s dominant strategy leads to an outcome worse for both than cooperation.
- Cartel
- A cartel is a group of firms that agree to restrict total output to raise their joint profit.
- Joint-Profit Maximisation
- Joint-profit maximisation is the output choice that makes the firms’ combined profit as large as possible, the monopoly output for the industry.
Oligopoly and Game Theory FAQ
Why is the Nash outcome not the cell with the highest total profit?
The stable cell is the one no firm wants to leave given its rival’s choice. At the highest-total cell each firm can gain by producing more while its rival holds back, so that cell is not stable.
Why do cartels tend to collapse?
Each member gains by secretly producing more than its quota, because it collects the extra revenue while the price fall is shared. Since every member reasons the same way, output rises towards the Nash level.
How does welfare compare across market structures?
With the same demand and cost, competition gives the largest gain to society, the non-collusive oligopoly less, and a cartel or monopoly the least, because more output above marginal cost creates more surplus.
Does the prisoners’ dilemma show that self-interest serves society?
No. Its lesson is the opposite: each player’s individually rational choice leads to an outcome both would want to avoid. In statement sets the keyed reading is that individual and collective interests can diverge, not that oligopolies always behave like a single monopoly.
Exam move
Build a two-choice matrix from a linear demand curve, mark each firm’s best response with arrows, then solve the same market algebraically and compare the Nash and cartel outcomes. After each matrix, solve the same market algebraically to see the Nash and cartel outputs as formulas.
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