Game Theory and Oligopoly Profit - Online Tutor, Practice Problems & Exam Prep

In an oligopoly, firms are interdependent, meaning their profits depend on competitors' decisions. For example, in a duopoly, collusion can lead to maximum profits, similar to a monopoly. However, the incentive to cheat can reduce total industry profits, resembling a prisoner's dilemma. The Nash equilibrium occurs when both firms choose strategies that maximize their payoffs, often resulting in lower profits than if they had cooperated. This dynamic illustrates the balance between competition and cooperation, positioning oligopolies between monopolies and perfect competition in terms of market outcomes.

Oligopoly Profit

Alright, so now let's take what we've learned about game theory and apply it to an oligopoly situation. Right, so what we've learned so far, we've seen that in an oligopoly, a firm's profit will be dependent on the decisions, on the output decisions of their competitors, right? They're going to be dependent on each other, and this is called interdependence. The firms are said to be interdependent because they depend on each other to make their best choices. They can't make their best choice without considering what the other people are going to do. Okay, so let's dive into an example here. We've got Jack and Jill who own the only wells in a small town, right? So Jack and Jill are the only producers. We've got two producers, so this is a duopoly, a form of an oligopoly. Okay? So in our duopoly, Jack and Jill, they have no cost of pumping water, right? No cost. We're just keeping it simple, so their marginal cost is equal to 0, and average total cost is equal to 0. We're just not going to deal with cost here because it's just going to complicate anything in our discussion. Okay, so we've got a table here with our demand schedule and notice we've got some quantities and prices and just like we would expect, as the quantity increases, the price decreases, right? Or as the price decreases, quantity increases. This is what we expect with a demand curve, right? We've got the law of demand, a downward-sloping demand curve, and then we have these quantities and prices and then a column for our revenue. And in this case, the revenue is going to be the same as profit because there are no costs. We're just leaving that out. So let's go ahead and figure this out. So, this total revenue, right, this is just our price times our quantity, right, so all we did was multiply across, so 0 times 120 was 0, 10 times 110, 120 times 100 was 2,000, right? We just multiplied it across our price times our quantity to get our total revenues. Okay, so I want to point out some key points here.

First, let's talk about the maximum revenue. Notice here when the quantity is 60, the price is 60, we have the maximum revenue of 3,600, right? And this is what a monopoly would produce right here. So, whether or not you studied monopolies, monopolies have significant market power, and they can produce wherever they're going to maximize their profit. They're the only producer in the market, so they're going to maximize their profit just like this, right? They would produce here 60 quantity at a price of 60 to maximize their profit. Compare that to perfect competition, right? Remember when we learn perfect competition, they reach efficiency. There are so many competitors in that market, right? There would be so many suppliers that they would keep driving the price down because there's still money to be made, so more competitors would join and drive it all the way to a situation where price equals marginal cost, right? That's a situation that occurs in perfect competition, so we would basically end up where there's no profit, right and we're supplying this maximum amount of 120 here. Perfect competition would reach some efficient quantity where our marginal benefit equals our marginal cost, perfect competition, right, down here.

Okay, and if you're confused, you see a price of 0, don't get hung up on that. That's because we have no cost in this situation. We're just saying that the condition of perfect competition is going to be a greater quantity. So, how are we going to find what's the best situation for an oligopoly? The first thing we have to consider is collusion, right? If Jack and Jill were able to work together, well they could essentially act as a monopoly. They could each produce half of the monopoly quantity. So that could be probably the ideal situation for them would be something where they're colluding. So let's start here in this left column where we have some collusion where they both say, "Let's produce 30 gallons to get the maximum profit in total." The total maximum profit will be highest, or the total profit will be highest.

So let's see what happens. If they're both producing 30 gallons, well the total quantity is going to be 30 that Jack produces, the 30 Jill produces, we're going to have 60 total gallons, right? So what's the price when there's 60 gallons on the market? 60 gallons on the market, a price of 60, right? That's what we have in our demand schedule, so the price equals 60. Knowing this, we can calculate their profit. We've got no costs, so their revenue will be their profit in this case. Let's go ahead and check that out. So Jack's profit is going to be the 30 units he sells times the $60 price. Well, that's going to give him 30 times 60 is 1800 in profit. Jack's profit is 1800. Jill also sells 30 units at a price of 60 and she also gets 1800.

Let's go underneath this table right here, let's do a column for, or a row for total profit. What's the total profit between the two of them? Well, that's the sum of the 1800 plus the 1800, that's gonna give us 3,600 in total profit, right? 3,600 total profit, and guess what? That's equal to our monopoly profit right here. That's what we expected. They took that monopoly profit and split it down the middle by each producing 30 gallons. But remember when we're colluding, there's that incentive to cheat. Jill can consider expanding her output. Knowing that Jack plans on cooperating, Jill can say, "Hey, if instead of producing 30, maybe I can make more money if I produce 40 gallons instead." So let's see what happens if Jill decides to cheat. This is going to be a situation where Jill cheats on their collusive agreement to each produce 30. So now let's see what happens. Jack produces 30. Jill produces 40. Well, that's going to be a total quantity of 30 from Jack, 40 from Jill, gets us to a total quantity of 70. So now the price is going to change. There's a higher quantity on the market, there's got to be a lower price to clear that and what do we see? When there's a quantity of 70, our price is 50 over here. So the price now is 50. Jill produced more than the collusive agreement and now it dropped the price down to 50.

So let's see what happens in this situation. Jack still produced 30 gallons, right? So Jack's profit is going to be the 30 gallons times this price of 50. He's no longer getting $60 per gallon, he's getting 50, and he's going to have 1500 in profit. 30 times 50 is 1500. What about Jill? Well, Jill produced 40, right? Her quantity is 40 that she sold at this $50 price, and guess what? Jill comes out with $2,000 in profit. Jill got more profit by cheating here, right? So this is that incentive to cheat we were talking about. By increasing her quantity, she took a little bit from Jack, and now she has a higher profit, but notice our total profit in the industry. The total profit is going to be the 1500 plus the 2,000, well total profit is now 3,500. The total profit decreased. There was a better situation for the producers in total when they colluded, and there was 3,600 in total profit. Notice at a quantity of 70, we've got a price of 50 and a profit of 3,500 just like we saw there, except now it's split between Jack and Jill, 1500, right?

So now what about this final situation? Jill thought about cheating. What if at the same time Jack had thought about cheating too? They both considered cheating. Alright, so now we're in this final column where both cheat, and they both. Well, we've got 40 plus 40 equals 80 in total quantity, right? What price do we have when 80 is the quantity on the market? Well, here's 80, a price of 40 when there's a quantity of 80. So we're going to have a price of 40. So let's check this out. What's going to happen to profit now? Let me get out of the way here, so we can fill in these boxes. We've got Jack's profit, right? Jack produced 40 units and he's selling them at a price of $40, and he's going to get $1600. 40 times 40 is 1600 and the same thing for Jill. 40 units at $40, and she's also going to get $1600. So what's the total profit in this case? Well, the total profit is 1600 plus $1,600. So notice that the total profit for the industry keeps decreasing, and in this case where they both cheat, we end up where both of them are worse off. If they had colluded, they would have both had 1800. If they both cheat, they're both down to 1600. What does this sound like to you? This is something we've gone over before. This sounds like a prisoner's dilemma. So let's pause here, and then in the next video, we'll fill out a payoff matrix using this information and see how the whole game theory relates to everything we just talked about. Alright, let's do that now.

Oligopoly Profit

Alright, guys, so now we're here at the bottom of the page in our payoff matrix. Let's go ahead and take all that information that we just gathered in our different situations and put it into our payoff matrix. Okay, so let's start with the situation where they were colluding, right? When they both produced 30 gallons, Jack's decision was to produce 30 gallons, Jill's decision was to produce 30 gallons. Well, what was their profit? Jack had $1800 in profit, and Jill had $1800 in profit, right? So notice how we're filling out a payoff matrix using this information that we just came up with. We're going to have those decisions, how much they are going to produce, and the payoffs based on those decisions. Okay?

How about that second situation where Jack produces 30 and Jill produces 40? Well, when Jack produces 30, Jill produces 40, that was the situation where Jill's taking some of Jack's revenue, right? And coming out on top. So Jack's income or profit will be $1500 in that case. Jill's profit will be $2000, right? That's what we calculated up here for Jack and Jill's profit when Jack produces 30 and Jill produces 40. Well, it would be the opposite, right? What if Jack produced 40 and Jill produced 30? We would have a similar situation, it would just be flipped, right? In that case, when Jack produces 40 and Jill produces 30, Jack comes out with $2000, right? And Jill gets $1500 over here, right? Because we're just flipping who was the cheater.

And then last but not least, we've got the situation where they both cheat and both produce 40 gallons, right? So that's going to be this box right behind me in the bottom right corner, and we had profits over here, right? We calculated Jack and Jill's profit to be $1600 each, so that would be $1600 for Jack and $1600 for Jill, right? So we filled in our payoff matrix. I'm going to go ahead and get out of the way, and let's use our check and X method to find dominant strategies and a Nash equilibrium. Okay? Let's check it out now.

Alright, so let's do this. Let's start with Jack, okay? So for Jack's decision, he has to think about what he would do based on Jill's decisions, right? So Jill decides to produce 30 gallons, Jack, what will Jack do? When Jill produces 30 gallons, well we saw, right? Jack wants to cheat. He's going to get more profit when he cheats, right? He'll produce 40 gallons and get $2000 rather than 30 gallons and get $1800. So we're going to put a check over here for Jack's decision when Jill produces 30. What about when Jill produces 40? If Jill produces 40, Jack either has to choose between $1500 or $1600, right? He can produce 30 and get $1500 or produce 40 and get $1600, so his better choice is to produce 40, right? So what do we see? We already see that Jack has a dominant strategy to produce 40, right? We have this column right here with two check marks, so we know that's a dominant strategy for Jack.

Okay, let's try Jill now. So Jill, she's first going to think what if Jack produces 30? So if Jack produces 30, I can produce 30 and get $1800 right here, or Jack can produce 30 and I'll produce 40 and get $2000. So Jill is going to want to cheat, right? Jill will cheat and produce 40, and that is why we're going to put an X in that box. What about if Jack produces 40? Again, the same thing. If Jack produces 40, Jill has to choose between making $1500 or $1600. Well, guess what Jill's going to pick? Jill's going to pick the $1600, right? Rationally, she's going to pick the one with more money. What do we see? We've got two X's in the same row, right? So now that we've got two X's in the same row, we know that that's also a dominant strategy, right? So Jack's dominant strategy is 40 gallons. Right? Jill's dominant strategy is also 40 gallons. And what about our Nash equilibrium? Our Nash equilibrium is a box that has both a check and an X, right? There's a box with a check and an X right here. That is our Nash equilibrium. Nash equilibrium is going to be this box right here, right? Where they're both earning $1600.

So I'm coming back in now. So what do we see? The Nash equilibrium was something like a prisoner's dilemma, right? If they had been able to cooperate, they would have both made $1800, but they both end up cheating and end up in this situation where they earn $1600, right? And that's because they're making their best choices based on what their competitors would do. So what does that do? It leads us to a situation where an oligopoly is producing somewhere in between the monopoly and perfect competition, right? Because of this interdependence and uncertainty of what your opponents are going to do. Cool? Alright. Let's go ahead and move on to the next video.

Here’s what students ask on this topic:

What is the Nash equilibrium in an oligopoly?

The Nash equilibrium in an oligopoly occurs when each firm chooses a strategy that maximizes its payoff, given the strategies chosen by other firms. In this state, no firm can improve its profit by unilaterally changing its strategy. For example, in a duopoly where two firms are deciding on output levels, the Nash equilibrium is reached when both firms produce quantities that, given the production level of the other, yield the highest possible profit. This often results in lower profits than if the firms had colluded, as each firm has an incentive to cheat to increase its own profit, leading to a situation similar to the prisoner's dilemma.

How does game theory apply to oligopoly markets?

Game theory applies to oligopoly markets by analyzing how firms' decisions are interdependent. In an oligopoly, each firm's profit depends on the actions of its competitors. Game theory models, such as the prisoner's dilemma, illustrate how firms might choose strategies like collusion to maximize joint profits. However, the incentive to cheat can lead to non-cooperative outcomes, reducing total industry profits. The Nash equilibrium concept helps predict the outcome where firms choose their best strategies given the strategies of others, often resulting in a balance between competition and cooperation.

What is the prisoner's dilemma in the context of an oligopoly?

The prisoner's dilemma in the context of an oligopoly describes a situation where firms would benefit from cooperating (e.g., colluding to set higher prices) but have an incentive to cheat to increase their own profits. If both firms cheat, they end up worse off than if they had cooperated. For example, if two firms agree to limit production to keep prices high, one firm might secretly increase output to gain more market share. If both firms do this, the market price falls, and both firms earn lower profits, illustrating the dilemma.

How does collusion affect profits in an oligopoly?

Collusion in an oligopoly can lead to higher profits for the firms involved, similar to a monopoly. By agreeing to limit production or set prices, firms can maximize their joint profits. For example, if two firms in a duopoly collude to produce a total quantity that maximizes industry profit, they can achieve higher prices and profits. However, the incentive to cheat on the collusive agreement can undermine this arrangement, leading to increased output, lower prices, and reduced profits for all firms involved.

What is the difference between perfect competition and oligopoly in terms of market outcomes?

In perfect competition, many firms produce identical products, leading to a market price equal to marginal cost and zero economic profit in the long run. The market reaches an efficient quantity where marginal benefit equals marginal cost. In contrast, an oligopoly consists of a few interdependent firms. These firms have some market power and can influence prices. The market outcome in an oligopoly lies between that of a monopoly and perfect competition, with higher prices and lower quantities than perfect competition but lower prices and higher quantities than a monopoly.