Game Theory and Oligopoly Profit: Videos & Practice Problems

In an oligopoly, firms are interdependent, meaning their profit outcomes depend significantly on the decisions made by their competitors. This interdependence is crucial in understanding how firms operate within this market structure. A classic example of this is a duopoly, where only two firms exist, such as Jack and Jill, who own the only wells in a small town. In this scenario, both firms have no costs associated with pumping water, simplifying the analysis as both marginal and average total costs are zero.

When analyzing their demand schedule, it becomes evident that as quantity increases, price decreases, adhering to the law of demand. The total revenue, which equals profit in this case due to the absence of costs, is calculated by multiplying price by quantity. For instance, when the quantity is 60, the price is also 60, leading to a maximum revenue of 3,600, which is the same profit a monopoly would achieve by producing at this quantity.

In contrast, perfect competition leads to a situation where price equals marginal cost, resulting in no economic profit. In an oligopoly, firms can maximize their profits through collusion, effectively acting as a monopoly. If Jack and Jill agree to produce 30 gallons each, they can achieve a total profit of 3,600, mirroring the monopoly profit. However, this collusive agreement presents an incentive to cheat, as one firm may increase output to gain a larger share of the market.

For example, if Jill decides to cheat and produces 40 gallons while Jack sticks to 30, the total quantity rises to 70, causing the price to drop to 50. Jack's profit decreases to 1,500, while Jill's profit increases to 2,000, demonstrating the temptation to deviate from collusion. The total industry profit declines to 3,500, indicating that while individual profits may rise through cheating, the overall profit for both firms diminishes.

In a scenario where both firms cheat and produce 40 gallons each, the total quantity reaches 80, leading to a price of 40. Here, both Jack and Jill earn 1,600, resulting in a total profit of 3,200. This outcome illustrates the prisoner's dilemma, where both firms are worse off than if they had cooperated. The dynamics of collusion and the temptation to cheat highlight the complexities of decision-making in oligopolistic markets, emphasizing the delicate balance between cooperation and competition.

In analyzing the payoff matrix for a duopoly scenario involving Jack and Jill, we begin by examining their production decisions and the resulting profits. When both collude and produce 30 gallons, they each earn a profit of $1800. If Jack produces 30 gallons while Jill produces 40 gallons, Jack's profit decreases to $1500, while Jill's profit increases to $2000, as she captures more market share. Conversely, if Jack produces 40 gallons and Jill produces 30 gallons, Jack's profit rises to $2000, and Jill's profit falls to $1500, illustrating the competitive nature of their decisions.

In the case where both produce 40 gallons, their profits settle at $1600 each. This scenario highlights the concept of a Nash equilibrium, where both players make optimal decisions based on the expected actions of the other. To determine dominant strategies, we analyze Jack's choices: if Jill produces 30 gallons, Jack maximizes his profit by producing 40 gallons, earning $2000 instead of $1800. If Jill produces 40 gallons, Jack again opts for 40 gallons, earning $1600 over $1500. Thus, Jack's dominant strategy is to produce 40 gallons.

Similarly, Jill's analysis reveals that if Jack produces 30 gallons, she can increase her profit to $2000 by producing 40 gallons. If Jack produces 40 gallons, Jill also chooses to produce 40 gallons for a profit of $1600. Therefore, Jill's dominant strategy is also to produce 40 gallons. The Nash equilibrium occurs in the scenario where both produce 40 gallons, resulting in a profit of $1600 each, despite the potential for higher profits through cooperation.

This situation exemplifies the prisoner's dilemma, where individual rational choices lead to a less optimal collective outcome. In an oligopoly, the interdependence of firms results in production levels that fall between those of a monopoly and perfect competition. The presence of competition, even among a few firms, reduces the maximum profit achievable by a monopoly, pushing the market towards a more efficient quantity of production.