When Your Best Move Depends on Theirs
In oligopoly, profits depend not just on your choice but on your rival's. Game theory is the mathematics of that interdependence.
The payoff matrix lays out every combination of choices and each player's resulting profit. The classic business game is the pricing dilemma between two firms choosing High or Low prices:
| Rival: High | Rival: Low | |
|---|---|---|
| You: High | 10 / 10 | 2 / 12 |
| You: Low | 12 / 2 | 4 / 4 |
(read each cell as your payoff / rival's payoff)
Dominant strategy: a move that is best no matter what the rival does. Here, Low beats High whether the rival goes High (12 > 10) or Low (4 > 2) — so both firms cut prices.
Nash equilibrium: a pair of strategies where neither player gains by deviating alone. Both-Low is the Nash equilibrium — yet both firms would be better off at Both-High. Individually rational moves produce a collectively poor outcome: the prisoner's dilemma in a suit.
Why don't firms just agree to keep prices high? Explicit collusion (a cartel) is illegal in most jurisdictions — and internally unstable, since each member profits by secretly cheating. But when the game repeats indefinitely, cooperation can survive without any agreement: undercut today and your rival punishes you tomorrow. The shadow of the future disciplines the present — which is why regulators watch mature, stable oligopolies so closely even without a smoking-gun contract.
Tip: To find a Nash equilibrium, test each cell: can either player improve by changing only their own move? If neither can, it's Nash. Both-Low passes; Both-High fails because each firm gains by undercutting (12 > 10).
Common pitfall: Assuming the equilibrium is the best outcome. The prisoner's dilemma's whole point is the opposite: individually rational moves lock both players into a collectively worse cell.