When Your Best Move Depends on Theirs
In oligopoly, profits depend on your rival's choices as much as your own. Game theory is the mathematics of this strategic interdependence.
The payoff matrix lays out every combination of choices and resulting profits. Consider two firms choosing High or Low prices:
| Rival: High | Rival: Low | |
|---|---|---|
| You: High | 10 / 10 | 2 / 12 |
| You: Low | 12 / 2 | 4 / 4 |
Cells show: your payoff / rival's payoff. A dominant strategy is a move that is best no matter what the rival does. Here, Low beats High whether the rival plays High () or Low (). Both firms face this incentive and cut prices.
Common pitfall: Assuming the equilibrium is the best outcome. The prisoner's dilemma proves that individually rational moves can lock both players into a collectively poor outcome.
Escaping the Dilemma
A Nash equilibrium is a pair of strategies where neither player gains by deviating alone. In our matrix, Both-Low is the Nash equilibrium. Both-High fails because each firm gains by undercutting ().
| Concept | Definition | Business Meaning |
|---|---|---|
| Dominant Strategy | Best move regardless of rival | Forces price cuts |
| Nash Equilibrium | Stable state, no unilateral deviation | The default outcome |
Why don't firms just agree to keep prices high? Explicit cartels are illegal and internally unstable since members profit by cheating.
However, when the game repeats indefinitely, cooperation can survive. Undercut today and your rival punishes you tomorrow. The shadow of the future disciplines the present, which is why regulators closely monitor stable oligopolies.