Game Theory Fundamentals
Introduction to Game Theory
What Is Game Theory?
Life is full of situations where your best move depends on someone else's. Choosing which checkout line to join at the grocery store, negotiating a salary, or even deciding where to go for dinner with a friend involves thinking about what others will do. This is the world of strategic interaction, and game theory is the tool we use to understand it.
Game theory is a technique used to analyse situations, such as the prisoner's dilemma, where any action you take affects, and is affected by, the actions of others - known as strategic interdependence.
At its core, game theory is the study of how and why we make decisions when our success is intertwined with the decisions of others. The "games" in game theory aren't just board games or sports. They can be any scenario involving two or more decision-makers where the outcome for each one depends on the actions of all. It helps us map out these situations to see the potential outcomes and make more informed choices.
The Building Blocks of a Game
To analyze any strategic situation, we first need to break it down into its core components. Every game, whether it's a business negotiation or a simple coin toss, has three essential elements.
Players
noun
The decision-makers in the game. A player can be an individual, a company, a country, or any entity making a choice.
Next, we have strategies.
Strategy
noun
A complete plan of action a player will take. It outlines what a player will do in every possible situation within the game.
Finally, every game has payoffs.
Payoff
noun
The outcome or consequence a player receives after all players have chosen their strategies. This could be money, points, utility, or any other measure of value.
Let's see these in action. Imagine two coffee shops, "The Daily Grind" and "Espresso Yourself," are the only ones in a small town. They each need to decide whether to keep their prices the same or lower them to attract more customers.
Here, the players are the two coffee shops. Their strategies are to either "Lower Prices" or "Keep Prices Same." The payoffs are the profits they make, which depend on the combination of strategies they both choose.
Types of Games
Not all games are played the same way. The biggest distinction comes down to whether players can work together.
Cooperative Games: In these games, players can form alliances and make binding agreements, like signing a contract. The focus is on what groups of players can achieve together, and how they should split the rewards.
Think of two companies deciding to co-invest in a new technology. They can sign a legal agreement to share the costs and the future profits. The challenge isn't about outsmarting each other, but about finding a fair and mutually beneficial arrangement.
Non-Cooperative Games: Here, players act independently. They can't make binding agreements and must make their decisions on their own, even if they communicate. The focus is on predicting an individual player's actions and the resulting outcomes.
Our coffee shop example is a non-cooperative game. Even if the owners talk, there's nothing stopping one of them from going back on their word to gain an advantage. Most situations we analyze in game theory, from auctions to international politics, fall into this category.
Understanding these basic elements—players, strategies, payoffs, and the type of game—allows us to start mapping out the strategic landscape of any interaction. It’s the first step toward thinking like a game theorist.