ECON1001 · Introductory Microeconomics
Game Theory & Oligopoly
Week 9 handles markets with a handful of interdependent firms. With few firms and high barriers, each firm's best move depends on rivals, so we use game theory: players, actions, payoffs in normal form. A dominant strategy is best regardless of the other player; a Nash equilibrium is a profile where no player can profitably deviate. The classic result is the prisoners' dilemma, where individually rational choices leave both worse off — the logic behind price wars and cartel breakdown. Sequential games are solved by backward induction, and commitment can change outcomes.
What this chapter covers
- 01Oligopoly features: few firms, interdependence, temptation to collude; cartels
- 02Game elements and the normal (matrix) form
- 03Dominant strategy and dominant-strategy equilibrium
- 04Nash equilibrium and best responses; equilibria stated in strategies
- 05Prisoners' dilemma: individually rational, jointly worse
- 06Escaping the dilemma through repeated interaction
- 07Sequential games and backward induction
- 08Commitment, first- and second-mover advantage, coordination games
Dominant strategy and Nash equilibrium in a pricing game
- 2 marks · F1 dominant strategyFirm 1: if Firm 2 plays High, Low (10) beats High (8); if Firm 2 plays Low, Low (4) beats High (2). So Low dominates for Firm 1.
- 2 marks · F2 dominant strategyBy symmetry, Firm 2's payoffs give Low (10 > 8 and 4 > 2) as its dominant strategy too.
- 2 marks · Nash equilibriumBoth playing their dominant strategy gives the unique Nash equilibrium (Low, Low) with payoffs (4, 4); neither can profitably deviate.
- 2 marks · dilemma explanationIt is a prisoners' dilemma because (High, High) gives (8, 8), which is jointly better, yet each firm has a private incentive to undercut, so cooperation is not self-enforcing.
Key terms
- Dominant strategy
- An action that yields a player the best payoff regardless of what the other players choose; if every player has one, their combination is a dominant-strategy equilibrium.
- Nash equilibrium
- A strategy profile in which each player's choice is a best response to the others, so no player can gain by deviating alone; a game may have zero, one, or several.
- Prisoners' dilemma
- A game whose Nash equilibrium is not jointly best: each player's dominant strategy leaves both worse off than mutual cooperation, which is not self-enforcing.
- Cartel
- A group of firms acting together to restrict output and raise price toward the monopoly outcome; unstable because each member is tempted to cheat, and usually illegal.
- Backward induction
- The method of solving a sequential game by reasoning from the final decisions back to the first, choosing each player's best move given what follows.
- Commitment
- A credible move that removes one's own future options to change the rival's best response and improve one's payoff — the 'burn the boats' logic.
Game Theory & Oligopoly FAQ
What is the difference between a dominant-strategy equilibrium and a Nash equilibrium?
A dominant strategy is best no matter what the rival does, so a dominant-strategy equilibrium is automatically Nash. A Nash equilibrium only requires each strategy to be a best response to the others' actual choices, so Nash equilibria can exist even when no one has a dominant strategy.
Why do firms in a prisoners' dilemma end up worse off?
Because each follows its private incentive to undercut or defect, which is individually rational. The combination of those rational choices lands them in the mutually worse outcome, even though cooperation would benefit both, because cooperation is not self-enforcing in a one-shot game.
How can repeated interaction sustain cooperation?
When the same firms meet repeatedly, the threat of future punishment for cheating can outweigh the one-period gain from defecting. This makes cooperative strategies a credible equilibrium that the one-shot prisoners' dilemma cannot support.
Exam move
Practise reading payoff matrices fast: underline each player's best response to every rival action, and where both best responses meet is a Nash equilibrium. Distinguish carefully between a dominant strategy and a best response, and always express equilibria as strategy pairs. For sequential games, draw the tree and solve by backward induction, then check whether commitment or move order changes the result — first- and second-mover advantages are favourite exam twists.
