# Game Theory in Business

Business I · Economics of the Firm · https://tryals.app/learn/business-i/game-theory-in-business

## 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 ($12 > 10$) or Low ($4 > 2$). 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 ($12 > 10$).

| 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.

## Practice questions

6 of this lesson's 12 practice questions, with answers. The full set is in the app.

### 1. Order the steps for finding a Nash equilibrium in a 2×2 payoff matrix.

**Answer:**

1. Write each player’s payoff in every cell
2. For each rival strategy, mark your best response
3. Repeat the marking from the rival’s perspective
4. Find cells where both payoffs carry a best-response mark
5. Declare those cells the Nash equilibria

**Why:** The best-response marking method turns equilibrium-hunting into a mechanical scan, doubly-marked cells are exactly the Nash equilibria.

Page: https://tryals.app/practice/business-i/game-theory-in-business/order-the-steps-for-finding-a-nash-equilibrium-in-a-2-2-payoff-matrix

### 2. In the pricing game, Low is a dominant strategy for both firms. Why does that make the outcome predictable without knowing anything about what either firm believes?

A. Because a dominant strategy is the better reply whatever they do
B. Because the firms can observe each other’s prices before choosing
C. Because both firms have agreed in advance to price Low
D. Because dominance means the strategy gives the highest possible payoff available in the game

**Answer:** A. Because a dominant strategy is the better reply whatever they do

**Why:** Dominance removes the need to predict anyone. That is what makes it the strongest solution concept, and why the prisoner’s dilemma outcome is so robust despite being worse for both.

Page: https://tryals.app/practice/business-i/game-theory-in-business/in-the-pricing-game-low-is-a-dominant-strategy-for-both-firms-why

### 3. Which conditions help sustain tacit cooperation (high prices) in a repeated oligopoly game?

A. Firms value future profits highly
B. The game repeats with no known end date
C. The market is about to disappear next quarter
D. Firms can quickly detect a rival’s price cut

**Answer:** A. Firms value future profits highly; B. The game repeats with no known end date; D. Firms can quickly detect a rival’s price cut

**Why:** Cooperation lives on the shadow of the future: indefinite repetition, fast detection, and patience. A known endgame unravels it, cheat in the last period, then the one before, all the way back.

Page: https://tryals.app/practice/business-i/game-theory-in-business/which-conditions-help-sustain-tacit-cooperation-high-prices-in-a

### 4. Two petrol stations on the same corner match each other's prices within minutes, day after day, without ever meeting. Is that collusion?

A. Not legally; repetition teaches that undercutting is punished
B. Yes, but only if the two stations share an owner
C. Yes, since identical prices can only result from an agreement
D. No, because prices in perfect competition are always identical

**Answer:** A. Not legally; repetition teaches that undercutting is punished

**Why:** The shadow of tomorrow's retaliation does what a contract would, so the cooperative outcome arrives without anyone agreeing to it, tacit collusion. That is precisely why competition authorities find it so hard to prosecute: the structure is guilty, and no one made a phone call.

Page: https://tryals.app/practice/business-i/game-theory-in-business/two-petrol-stations-on-the-same-corner-match-each-others-prices

### 5. Order the unraveling of a cartel, from formation to collapse.

**Answer:**

1. Rivals agree to keep prices high
2. Each member notices cheating would boost its own profit
3. One firm secretly undercuts the agreed price
4. Others detect the cheating and retaliate with cuts
5. Prices collapse to the competitive level

**Why:** The cartel’s poison is internal: every member’s private incentive points against the collective deal.

Page: https://tryals.app/practice/business-i/game-theory-in-business/order-the-unraveling-of-a-cartel-from-formation-to-collapse

### 6. Sort each business situation by the game it most resembles.

**Answer:**

- Prisoner’s dilemma: Two supermarkets locked in a price war neither wants, Rival ad blitzes that cancel out but drain both budgets
- Coordination game: Tech firms choosing a common charging standard
- First-mover game: Racing to open the first store in a new district

**Why:** Dilemmas punish mutual defection, coordination games reward matching, and first-mover games reward speed.

Page: https://tryals.app/practice/business-i/game-theory-in-business/sort-each-business-situation-by-the-game-it-most-resembles