Oligopoly, Monopoly, and Competitive Markets: Models and Comparisons

Oligopoly and Game Theory

Sequential-Move Games and Subgame Perfect Nash Equilibrium

In microeconomics, oligopoly markets are often analyzed using game theory. Sequential-move games involve players making decisions one after another, and the solution concept used is Subgame Perfect Nash Equilibrium (SPNE).

• Follower's Strategy: The follower chooses the optimal action in response to every possible action taken by the leader.

• Leader's Strategy: The leader anticipates the follower's optimal response and chooses its own optimal strategy accordingly.

Oligopoly Market: A market with a few sellers, each having partial influence over the market's total output or price. Sellers are viewed as players in a game.

• Duopoly: A special case of oligopoly with two sellers.

• Each seller's decisions affect the market outcome.

Chapter 12: Monopolistic Competition and Oligopoly

Oligopoly Models

Three main models are used to analyze oligopoly behavior:

• Cournot Model: Firms choose output levels simultaneously, treating competitors' output as fixed.

• Bertrand Model: Firms compete by setting prices.

• Stackelberg Model: Firms move sequentially, with one firm acting as a leader and the other as a follower.

In the Cournot model, the strategy of each firm is to choose an output level, and the payoff is the profit. The equilibrium reached is called the Cournot Equilibrium, a Nash Equilibrium in output choices.

Interconnected Payoffs in Oligopoly

• Total output produced by all firms determines the market price.

• Each firm's profit depends on both its own output and the output of competitors.

Example: Europe’s Energy Crisis

The European natural gas market is an oligopoly, with major suppliers like Russia, Norway, LNG sources, and Algeria. Their profits are interconnected through the market price of natural gas. Geopolitical events, such as the war in Ukraine, can shift market shares and profits among these suppliers.

• Norway's profits increased significantly due to changes in supply and price.

Monopoly Model: Review Example

Monopoly Equilibrium Calculation

Consider a market with demand $Q(p) = 1000 - 2p$ and a monopoly firm with cost $C(q) = 200q$.

• Inverse Demand: $p(q) = 500 - 0.5q$

• Total Revenue: $R(q) = p(q)q = 500q - 0.5q^2$

• Marginal Revenue: $MR(q) = \frac{dR}{dq} = 500 - q$

• Marginal Cost: $MC(q) = \frac{dC}{dq} = 200$

Set $MR(q^*) = MC(q^*)$:

• $500 - q^* = 200 \Rightarrow q^* = 300$

• $p(q^*) = 500 - 0.5 \times 300 = 350$

• Profit: $\Pi(q^*) = p(q^*)q^* - C(q^*) = 350 \times 300 - 200 \times 300 = 45000$

Competitive Market Model: Review Example

Competitive Equilibrium Calculation

Same demand and cost functions as above, but now many firms compete.

• Individual Supply Curve: Horizontal at $p = 200$

• Market Supply Curve: Also horizontal at $p = 200$

• Market Demand: $Q(p) = 1000 - 2p$

• At $p = 200$, $Q(200) = 1000 - 2 \times 200 = 600$

• Competitive Equilibrium: Price $= 200$, Quantity $= 600$

• Profit: Each firm earns zero profit since $p = AC$

Cournot Duopoly Model: Review Example

Cournot Equilibrium Calculation

Two firms with cost functions $C_1(q_1) = 200q_1$, $C_2(q_2) = 200q_2$ and market demand $Q(p) = 1000 - 2p$.

• Inverse Demand: $p(q) = 500 - 0.5q$, where $q = q_1 + q_2$

• Firm 1 Revenue: $R_1 = (500 - 0.5q_1 - 0.5q_2)q_1 = 500q_1 - 0.5q_1^2 - 0.5q_1q_2$

• Firm 1 Marginal Revenue: $MR_1 = 500 - q_1 - 0.5q_2$

• Firm 1 Marginal Cost: $MC_1 = 200$

• Firm 1 Reaction Function: $q_1 = 300 - 0.5q_2$

• Firm 2 Revenue: $R_2 = (500 - 0.5q_1 - 0.5q_2)q_2 = 500q_2 - 0.5q_1q_2 - 0.5q_2^2$

• Firm 2 Marginal Revenue: $MR_2 = 500 - 0.5q_1 - q_2$

• Firm 2 Marginal Cost: $MC_2 = 200$

• Firm 2 Reaction Function: $q_2 = 300 - 0.5q_1$

Solve the system:

• $q_1 = 300 - 0.5q_2$

• $q_2 = 300 - 0.5q_1$

• Solving yields $q_1 = q_2 = 200$

• Total output $q = 400$

• Equilibrium price: $p(q) = 500 - 0.5 \times 400 = 300$

• Profit for each firm: $\Pi_1 = \Pi_2 = 300 \times 200 - 200 \times 200 = 20000$

Comparisons: Monopoly, Cournot Duopoly, and Competitive Equilibrium

Summary Table

Market Structure	Total Output	Price	Total Profit
Monopoly	300	350	45000
Cournot Duopoly	400 (200 each)	300	40000 (20000 each)
Competitive Market	600	200	0

Key Comparisons

• Cournot vs Monopoly: Cournot equilibrium has higher total output, lower price, and lower total profit than monopoly.

• Monopoly as Collusion: If firms collude perfectly (cartel), they act as a monopoly. Cartels are illegal in the U.S. (e.g., OPEC).

• Cournot vs Competitive Market: Cournot equilibrium has lower total output, higher price, and higher total profit than a competitive market.

Additional info:

• Reaction functions in Cournot model show how each firm's optimal output depends on the other firm's output.

• Profit in competitive equilibrium is zero because price equals average cost.

• Collusion is unavailable in noncooperative games, so Cournot equilibrium is the typical outcome when firms act independently.