## Oligopolies and Tacit Collusion

### Oligopoly

• We’ve discussed how firms can raise profits above the competitive level by colluding
• Collusion amongst firms can be tacit or explicit
• The easiest way to model collusion is with oligopoly, which occurs when a small number of firms produce a homogeneous product
• For simplicity, we’ll assume that an oligopoly only consists of two firms (i.e. duopoly)
• Oligopolies must have mutual interdependence
• All firms must be aware of each other’s prices, and care about their actions

### Nash Equilibrium

• In order to better understand mutual interdependence, we need some game theory
• Nash equilibrium occurs when no player has incentive to unilaterally deviate from their current strategy
• A Nash equilibrium consists of a strategy for every player
• Suppose we want to determine if a set of strategies constitutes a Nash equilibrium
• We want to see if any player has incentive to unilaterally deviate from their current strategy (i.e. can one player increase profit by unilaterally changing their strategy)
• We’ll do this for every player in the game
• If no player can better their profit unilaterally, then we have found a Nash equilibrium

### Example

• Consider the following game between player 1 and player 2
• Each player can select either a high price (H) or a low price (L)
• The Nash equilibrium occurs when both player 1 and player 2 price high, resulting in a payoff of 4 to each player
• Neither player can unilaterally deviate and increase their profit

### Example Question

Would it be easy or difficult to maintain effective collusion if two dupolists faced the following profit matrix?

Firm B’s Action
High Price Low Price
Firm A’s Action High Price 1000, 150 700,100
Low Price 800, 50 500,75

Does there appear to be a dominant firm in this industry? Does Firm A have a dominant solution to this game? Does Firm B have a dominant solution to this game?

#### Solution

Firm A appears to be the dominant firm in this industry. High price is Firm A’s dominant strategy. Firm B does not have a dominant strategy. Nash Equilibrium is both firms charge high price.