Game theory is a branch of mathematics that studies strategic decision-making and the interactions between firms.

It is a powerful tool that can help you make better business decisions by understanding the behaviors and motivations of your competitors and customers.

In this beginner’s guide, we’ll delve into the history and basic concepts of game theory, as well as some real-world applications in business.

**History Of Game Theory**

The history of game theory can be traced back to the work of Austrian economist and mathematician, von Neumann, and economist, Morgenstern, who published the book “Theory of Games and Economic Behavior” in 1944.

This book laid the foundations for the modern study of game theory, which has since been developed and refined by many other notable figures such as John Nash, who was awarded the Nobel Prize in Economics for his work on equilibrium in non-cooperative games.

**Basic Concepts Of Game Theory**

Now, let’s delve into some of the basic concepts of game theory. One key concept is the strategic form of a game, which represents the decision-making process of two or more players who have to choose between different strategies.

For example, consider a game between two firms that are deciding how much to invest in advertising.

The strategic form of this game would look like a matrix with the strategies of each firm listed in rows and columns, and the payoffs listed in the cells.

The payoffs represent the profit or loss that each firm would incur depending on their own and their competitor’s strategies.

Another key concept is the normal form of a game, which represents the same information as the strategic form, but in a different way.

Instead of listing the strategies in rows and columns, the normal form lists the strategies for each player as a set of options, with the payoffs for each combination of options listed in a table.

Nash equilibrium is a concept that is central to game theory. It represents a situation in which no player has an incentive to change their strategy, given the strategies of the other players.

In other words, it is a stable state in which no player can benefit by changing their strategy unilaterally.

For example, consider the game of chicken, in which two players simultaneously decide whether to swerve or stay straight. If both players stay straight, they both get a payoff of 0.

If one player swerves and the other stays straight, the player who swerved gets a payoff of -10 and the player who stayed straight gets a payoff of 10.

If both players swerve, they both get a payoff of 5. In this game, the Nash equilibrium is for both players to stay straight, as neither player has an incentive to change their strategy given the other player’s strategy.

Mixed strategy equilibrium is a concept that extends the idea of Nash equilibrium to games in which a player has more than one pure strategy available.

A pure strategy is a strategy that is played with certainty, whereas a mixed strategy is a strategy that is played with some probability.

For example, consider a game in which a player can choose to play either strategy A or strategy B.

If the player plays strategy A with probability p and strategy B with probability (1-p), then they are playing a mixed strategy.

Mixed strategy equilibrium occurs when no player can improve their expected payoff by changing their mixed strategy.

**Applications Of Game Theory In Business**

Now, let’s look at some real-world applications of game theory in business. One classic example is price competition between two firms.

This is a game that can be represented in strategic form as a matrix with the strategies of each firm listed in rows and columns, and the profits for each firm listed in the cells.

In this game, each firm has to decide whether to charge a high price or a low price for their product. If both firms charge a high price, they both make a high profit.

If one firm charges a high price and the other charges a low price, the firm that charges the low price captures a larger market share and makes a higher profit, while the other firm makes a lower profit. If both firms charge a low price, they both make a lower profit.

The Nash equilibrium in this game is for both firms to charge a high price, as neither firm has an incentive to change their strategy given the other firm’s strategy.

However, if one firm decides to charge a low price in an attempt to capture a larger market share, they may be able to achieve a higher profit in the short run, even though it may not be an equilibrium outcome.

Another application of game theory in business is in oligopoly, which is a market structure in which a small number of firms dominate the industry. In an oligopoly, firms have to take into account the actions of their competitors when making decisions.

For example, consider the game of price competition between two firms in an oligopoly. In this game, each firm has to decide whether to charge a high price or a low price for their product.

If both firms charge a high price, they both make a high profit. If one firm charges a high price and the other charges a low price, the firm that charges the low price captures a larger market share and makes a higher profit, while the other firm makes a lower profit.

If both firms charge a low price, they both make a lower profit.

The Nash equilibrium in this game is for both firms to charge a high price, as neither firm has an incentive to change their strategy given the other firm’s strategy.

However, if one firm decides to charge a low price in an attempt to capture a larger market share, they may be able to achieve a higher profit in the short run, even though it may not be an equilibrium outcome.

Another application of game theory in business is in auctions, which are used to sell goods or services to the highest bidder.

There are several different types of auctions, including English auctions, Dutch auctions, and sealed-bid auctions. Game theory can be used to analyze the behavior of bidders in auctions and to understand how the design of the auction can affect the outcome.

Finally, game theory can also be applied to the negotiation process between two or more parties.

Negotiation is a common occurrence in business, and game theory can be used to understand how to negotiate effectively and to reach mutually beneficial agreements.

**Real-World Examples Of Companies Using Game Theory**

Game theory is not just a theoretical concept; it is also used by real companies to make strategic decisions and understand the behaviour of their competitors.

Here are a few examples of real companies using game theory: Apple and Samsung use game theory to analyze the smartphone market and predict each other’s actions; Amazon and eBay use game theory to analyze the online retail market and determine optimal pricing and marketing strategies; and Uber and Lyft use game theory to analyze the ride-hailing market and make strategic decisions.

**Apple and Samsung:**Apple and Samsung are two major competitors in the smartphone market. In order to understand each other’s behavior and make strategic decisions, they may use game theory to analyze the market and predict each other’s actions. For example, they may use game theory to predict how the other firm will respond to a price change or a new product launch, and to determine the optimal pricing and marketing strategy for their own products.**Amazon and eBay:**Amazon and eBay are two major online retailers that compete with each other for customers. They may use game theory to analyze the market and predict each other’s actions, such as how the other firm will respond to a price change or a new product listing. They may also use game theory to determine the optimal pricing and marketing strategy for their own products and services.**Uber and Lyft:**Uber and Lyft are two major ride-hailing companies that compete with each other for riders. They may use game theory to analyze the market and predict each other’s actions, such as how the other firm will respond to a price change or a new service offering. They may also use game theory to determine the optimal pricing and marketing strategy for their own services.

**Conclusion**

In conclusion, game theory is a powerful tool for understanding strategic decision-making and the interactions between firms.

By mastering the basic concepts and applying them to real-world business situations, you can make better decisions and achieve better outcomes.

If you’re interested in learning more about game theory and how it can benefit your business, consider signing up for a course on learnsignal.com.

**References:**

- An Introduction to Game Theory” by Paul R. Milgrom and John Roberts: https://www.econlib.org/library/Enc/IntroductiontoGameTheory.html
- “The Basics of Game Theory” by Ariel Rubinstein: https://plato.stanford.edu/entries/game-theory-basics/
- “Game Theory” by Ken Binmore: https://www.math.ucdavis.edu/~binmore/GameTheoryBook/gthome.html
- “Game Theory” by Vincent F. Hendricks: https://www.iep.utm.edu/gametheo/
- “Game Theory” by Michaelmas Term: https://ocw.mit.edu/courses/economics/14-74-game-theory-fall-2015/