One of the biggest challenges in running a business is making decisions. It would be easy if you had a crystal ball and knew the outcomes of each choice. Game theory is no crystal ball, but it can help you make good decisions with the information available to you.
Keep reading to find out how you can use Game Theory for decision-making and other aspects of running a business.
What Is Game Theory?
Game Theory definitions can be complicated and hard to understand. In this article, let's simplify it to the following:
Game Theory is a framework for understanding situations involving competition or strategic interaction.
Although we’re talking about the business context, Game Theory originates from the field of mathematics. In 1928, John von Neumann, a Hungarian-American mathematician, physicist, and engineer published the paper, “On the Theory of Games of Strategy.” Neumann's work culminated in the book, Theory of Games and Economic Behavior, which he co-authored with Oskar Morgenstern.
They explored how to find mutually beneficial solutions for two-person, zero-sum games or games where one player wins and the other loses. As you'll see, Game Theory can be applied in other scenarios as well.
Game Theory is useful in business because it can also be used to predict outcomes and to think through situations strategically.
Elements of Game Theory
One of the easiest ways to understand and apply Game Theory is by breaking it down to its five basic elements. They are:
- Game. This is the scenario, situation, or set of circumstances. For Game Theory to be useful, the “game” must involve two or more parties that are in a competitive situation. And their actions must have an impact on each other.
- Players. These are the individuals, stakeholders, or parties involved in the game. They can make decisions and take action. Game Theory assumes that players are rational. That means they want to get the best possible outcome in the game.
- Strategy. This refers to the plan of action each player decides to take.
- Payoff. This is the reward or payout a player receives after carrying out their strategy. Payoffs may come in the form of money or some other quantifiable outcome.
- Equilibrium. This is when all players have carried out their strategies and the outcomes take place.
Types of Games in Game Theory
As you can imagine, the “games” in Game Theory can come in many shapes and sizes. Here are just a few of the types of games:
Symmetric/Asymmetric
A game can be either symmetric or asymmetric. A symmetric game is where both players have the same strategies at their disposal, and the payoffs for each strategy are the same.
In an asymmetric game the strategy isn't identical for both players. Each player has a different strategy they may employ. Or, they may have the same possible strategies, but the payoffs are different for each player.
Simultaneous/Sequential
A simultaneous game is one where all players move at the same time. A game where players don’t know what the other player’s earlier actions are is also considered “simultaneous.” The point is that they don’t know the other player’s move until after they’ve carried them out.
A sequential game (also known as a dynamic game) is where players know the other player’s earlier actions. Even if they know very little about the first player’s earlier actions—and don't have complete information about it—the game is still considered sequential.
Cooperative/Non-Cooperative
A game may also be classified as either cooperative or non-cooperative. In a cooperative game, players can form a coalition or alliance to achieve their desired payoffs. In contrast, in a non-cooperative game, players are in competition with each other. They can have alliances only if there’s an external authority enforcing it. This external force could be a contract law, for example.
Uses and Applications of Game Theory
Although originating from the field of mathematics, Game Theory has wide applications in various fields. It’s applied in economics, psychology, biology, politics, war, and business.
Game Theory is useful for:
- understanding interactions among different stakeholders in a situation
- explaining past events and choices made by individuals, organizations, or institutions
- predicting outcomes involving two or more actors
- decision-making when the possible outcomes are affected by the actions of others
As you can see, Game Theory can be pretty useful!
Examples of Game Theory
It’s easier to understand how Game Theory can be useful when we consider some specific examples. Here are a few of the most commonly-known Game Theory examples:
1. The Prisoner's Dilemma
In the Prisoner’s Dilemma, the players are Prisoner A and Prisoner B. They've got both been arrested for bank robbery, and the police are pressuring them to confess.
The possible payoffs involve the length of their sentences. If a player confesses but the other doesn't, then the player who confessed gets a much shorter sentence. The one who keeps their mouth shut gets the longest sentence. If both players confess, they both get a shorter jail sentence. If neither one confesses, both will have a long jail time. The payoffs can be represented by this table:
If both prisoners confess, then they only serve jail time for one year. This is a win-win situation example. That is, the payoffs are the best for both players if they both confess.
If Prisoner A confesses, but Prisoner B stays silent, then Prisoner A goes to jail for five years and prisoner B serves for 10. Similarly, if Prisoner B confesses, but Prisoner B does not, then Prisoner B gets out after five years, while Prisoner A goes to jail for 10.
And if both refuse to confess, then they both go to jail for 15 years. This is a no-win scenario or, as the name implies, both players lose.
Looking at the matrix, it’s obvious that the best strategy for both prisoners is to confess. But here’s the thing: Neither one knows what the other will decide to do. In other words, they can't form an alliance and cooperate with each other by both agreeing to confess.
The opposite is also true. Neither one knows if the other will betray them and confess. This is an example of a symmetric, simultaneous, and non-cooperative game. It’s symmetric because both players’ strategies and the payoffs for each are identical. It’s simultaneous because they've got to make their decisions at the same time, without knowing what the other decides. And it’s non-cooperative because they can't intentionally form an alliance. (It can be argued that both prisoners may have a previous agreement to protect each other and keep silent. But one never knows if each one will, indeed, honor their commitment.)
Without knowing what the other player’s strategy is, the obvious choice is for a prisoner to confess. Even if the other prisoner were to stay silent, the confessor’s jail time would still be less than if they were to stay silent. This is what’s known as the Nash Equilibrium or the point where a player will choose a given strategy, no matter what the other player decides to do.
2. The Centipede Game
The Centipede Game also has two players and two strategies. But it’s a very different game than the Prisoner’s Dilemma, as you'll see.
In the Centipede Game, Player 1 and Player 2 take turns. At each turn, a player has a choice of two strategies:
- To end the game
- To add $2 to the pot and keep playing
If a player ends the game, they take $2 more than the other player. If a player adds to the pot and keeps playing, the pot grows but they run the risk of the other player choosing to end the game. But if they both cooperate and play the game through to the end of 50 rounds, then they split the pot 50-50. That is, they each get $100.
Working backwards, it seems that the most rational choice would be for Player 1 to end the game in the first round. They would get $2, and Player 2 would get nothing. That’s the win-lose scenario (or zero-sum game). One player takes all, and the other loses everything. In reality, scientists have found, people tend to end the game at around the midpoint, where each player gets some money—not quite $100 each but much better than zero.
This is an example of a symmetric, sequential, and non-cooperative game. It’s symmetric because both players have the same choice of strategies, and each strategy has the same payoffs. It’s sequential because they take turns deciding and they know what move the other player made. And it’s non-cooperative because again, while they may decide to cooperate and end the game with each one getting $100, there’s no guarantee that they'll both honor that.
3. The Dictator Game
This is another common game in Game Theory and the scenario is quite simple. As with the previous game, the Dictator Game has two players:
- the Sender
- the Receiver.
They don’t know each other. Learn more about the Dictator Game in this video.
Here’s the scenario: The Sender receives an amount of money, say $100. Next, the Sender must decide how much of that money to send to the Receiver. They've got full control of this amount. They can choose to keep all the money, give all of it away to the Receiver, or give any amount in between.
The Receiver doesn’t do anything at all. They can't influence the Sender’s actions. In fact, they don’t even know the Sender. They're a passive player in this game.
This is an example of an asymmetric, sequential, and non-cooperative game. It’s asymmetric because the Sender and the Receiver have different strategies available to them. And their payoffs aren't identical, either. It’s sequential because the Receiver would know if the Sender shares some money with them. And it’s non-cooperative because there’s no way for them to cooperate with each, for example, by agreeing to split the money in half.
Rationality dictates that the Sender would keep most, if not all, of the money. But in real-life experiments, researchers have found that the average Sender gives 25-35% of the money to the Receiver. Different factors play a role. For example, women tend to give more than men do. And Senders tend to give less if they have to earn the money.
This indicates that money isn’t the only payoff that people consider. In the Dictator Game, they may consider other payoffs, such as being perceived as generous rather than greedy by the researcher.
How to Apply Game Theory to Business: 3 Steps
I hope the above game theory examples have given you an idea of how you might apply Game Theory in business. As an example, let’s try to apply Game Theory to planning a business promotion or campaign.
Step 1. Identify the Key Elements of the Game
The first step is to list the different elements of the game. For our example, the elements are:
Game. The game or scenario is a special promo for Acme company.
Players. The players are Acme company and consumers. Consumers include both existing customers of Acme company, as well as new ones that may come in through the promotions.
Strategies. This is an asymmetric game in that Acme company and its buyers have different strategies. Acme company’s strategies include offering either a 50% discount or a 10% discount. The buyers’ strategies are to buy or not to buy.
Payoffs. The rewards for Acme company are increased number of sales, new customers, and wider exposure of their brand. Or the promo could mean smaller profit margins and cultivating a customer base that only buys during a sale. For the buyers, their payoffs include saving on Acme products and enjoying the benefits of Acme’s widget, buying a different product, or keeping their money and not buying anything.
Equilibrium. When the dust has settled, both players will decide if their choices have helped them achieve their goals. Acme company will have achieved their target gross sales and net profit or not. And the buyers will decide if they’ve made the right decision to buy or if they’ve wasted their money.
Step 2. Quantify the Payoffs in a Payoff Matrix
As we see above, Acme and its buyers have a number of payoffs, depending on which strategy they choose. And these payoffs aren’t always about money. Gross sales and profit margins are easy to quantify but attracting only discount-buyers is harder. Simply do your best to assign a number to the totality of the payoffs (both the pros and cons).
After you’ve done that, put the quantified payoffs in a matrix. It could look something like this:
At 10% off, if consumers buy, then the payoff for Acme would be 50. That represents the increase in sales, increase in new customers, and exposure, with a slight reduction in profits. The payoff for consumers who buy at this price point is represented by a 30. That stands for the payoff of enjoying Acme’s widget while saving a little bit.
If buyers don’t purchase at the 10% discount, then the payoff for Acme would be only 10. They don’t get more sales, new customers, or exposure. But then, they make the same profit margins on the sales that do come in. For consumers who don’t buy at this price point, the payoff is 0 because it’s status quo for them. They keep their money, but they continue to not enjoy the benefits of Acme’s product.
If buyers purchase at 50% off, the payoff is high for both parties. The payoff for Acme is 70 because they get a higher bump in sales and new customers, whom they can nurture in the long-term for a higher lifetime value. Consumers also get a higher payoff. They get to enjoy the product while keeping more of their money. And they feel good about being smart buyers. The scenarios where Acme offers a discount and consumers buy are win-win examples in business.
But if consumers don’t avail of the 50% discount, their payoff is actually a negative number. They miss out on the opportunity to acquire Acme’s product and to save money while doing so. Of course, we’re assuming that they want the product! For Acme, the payoff is still 10 if consumers don’t grab this offer.
Step 3. Analyze the Matrix and Make a Decision
Now, look at the matrix and see which strategy will give you the best payoff, keeping your goal in mind.
In this example, it’s clear that offering 50% off is the best strategy. If it attracts buyers, then the payoff is huge. But if not, then they don’t really lose anything.
Tips for Applying Game Theory to Business
Game Theory won’t always surface such a straightforward answer as our example above. Keep the following three tips in mind.
1. Use the Best Information Available
Your analysis, conclusions, and decisions are only as good as the information you've got at hand. And so, do your best to collect the best information before sitting down to analyze a situation using Game Theory.
With that said, don’t wait until you've got all the information and perfect information. That may only cause unnecessary delays. Do your best with the information at hand, knowing that it'll always be incomplete and imperfect.
2. Realize You Won’t Always Win
Game Theory doesn’t guarantee success. Neither does any other analytical framework. Success in Game Theory means making the best decision through analysis rather than through emotions or, worse, without clear reasons for choosing a particular course of action.
3. People Aren’t Always Rational
Game Theory assumes that people are rational (and act to maximize their payoffs), but researchers have seen that that isn't always the case. We can and often decide based on our feelings or intuitions. Some even rely on chance. So, if things don’t turn out the way you anticipated, this could be the reason why.
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Think Through Scenarios with Game Theory
By now I hope you can see that Game Theory is a useful lens for taking a comprehensive look at a situation. It helps you analyze each stakeholder’s motivations and desired payoffs. And it can help reveal the best strategy among different options.
Now that you know the answer to what Game Theory is, you can use it to understand past interactions, predict outcomes, and make the best decision with the information you've got available. Try it and see how it improves your analysis of a scenario.
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