Worked example
Worked example: The Prisoner's Dilemma in pricing
Your main rival just announced aggressive discounts in your premium segment. Do you match them or hold your price? This is the Prisoner's Dilemma wearing business clothes — here is the complete game-theory analysis, with every figure from the analyzer.
The setup
Two firms sell into the same premium segment. Each has two strategies: hold price, or match the discounts. The numbers below are each firm's annual profit in $millions — ours first, then theirs — for each combination of choices.
| Rival holds → Rival matches ↓ | Our profit | Rival's profit |
|---|---|---|
| Both hold price | $100M | $100M |
| We hold, rival matches | $60M | $130M |
| We match, rival holds | $130M | $60M |
| Both match discounts | $80M | $80M |
What the analysis finds
Matching discounts is a strictly dominant strategy. If the rival holds, matching earns $130M versus $100M from holding. If the rival matches, matching earns $80M versus $60M. Whatever the rival does, matching is better — "always better", as the analyzer labels it.
Since the rival's payoffs mirror ours, matching is dominant for them too. That pins the Nash equilibrium at both matching, earning $80M each. Neither firm can profit by changing its choice alone: if we unilaterally held price while they discounted, we would drop to $60M. The outcome is stable even though both firms would earn $100M if both held — $20M each left on the table, every year.
The analyzer reports this as a unique stable outcome driven by dominance, and names the gap: the equilibrium is worse for both players than the cooperative outcome. That gap is the definition of a dilemma.
How firms escape the trap
- Make the game repeated. The one-shot analysis assumes a single season. When the rivals meet every quarter, discounting invites retaliation, and cooperative pricing can sustain itself — this is why the analyzer's dynamic-game screen asks about horizons and competitor responses.
- Change the payoffs. Differentiation, switching costs and contracts make matching less attractive, which can dissolve a dominant strategy entirely.
- Commit visibly. A credible public commitment to hold price can move the rival's best response — Schelling's insight, and the reason commitment is a strategy, not a slogan.
One caution: agreeing prices with a competitor is illegal in most jurisdictions. The point of the analysis is to understand the pressure, not to collude — unilateral differentiation is the lawful escape route.
Questions people ask
What is the Prisoner's Dilemma in business?
It is any situation where two competitors each have an incentive to act in their own interest, and both end up worse off than if they had cooperated. A pricing war is the classic case: discounting is the safe choice against every rival move, yet when both sides discount, both earn less than if both had held price.
What is a Nash equilibrium in simple terms?
A pair of choices where neither side can improve by changing their own choice alone. In the pricing example below, both firms matching discounts is the equilibrium: holding price while the rival discounts costs you $40M, so neither side moves — even though both prefer the world where neither discounted.
This example is illustrative and provides decision support, not professional advice. Model a payoff matrix with your own figures in the analyzer. See the Terms & Conditions.