Basics of Game Theory

Welcome! I'm really looking forward to exploring game theory with you. Before we dive into the fun stuff, I'd love to know a little bit about you so I can make this session as useful as possible.

To help me tailor this session, what is your background in math or economics, and is there a specific field (like business, politics, or just general interest) where you want to apply game theory?

I'm comfortable with math/econ and want to see how it applies to politics and sociology.

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Basic Solution Concepts

Classic Examples

What is Game Theory?

At its heart, game theory isn't about board games like Monopoly or chess. Instead, it is the formal study of . This is just a fancy way of saying: situations where the outcome of your choice depends not only on what you do, but also on what other people do, and vice versa. It is the math of social interactions.

In politics and sociology, this is everywhere. Think of two rival nations deciding whether to build up their militaries, or two politicians choosing how to run their campaigns. Neither can make an optimal decision in a vacuum; they must actively anticipate what the other side will do.

Continue to the core components of a game (PAPI)

Let's dive straight into how game theorists actually deconstruct these social interactions. To model any strategic situation, we use a simple four-part framework known by the acronym PAPI: Players, Actions, Payoffs, and Information.

The PAPI Framework

Every single game, from chess to a nuclear standoff, is built on these four essential ingredients:

: These are the decision-makers. They can be individuals, political parties, corporations, or entire countries.
Actions: These are the moves or choices available to each player. For a political candidate, actions might be "run a positive campaign ad" or "run a negative smear campaign ad."
: These are the outcomes or rewards that players receive at the end of the game, based on the combination of actions chosen by everyone. In political science, we often measure payoffs not in money, but in "utility"—like votes gained, power secured, or policy goals achieved.
Information: This refers to what each player knows (and when they know it) about the rules, the other players, and the moves that have already been made.

Let's look at how this applies to a real political scenario. Imagine two rival nations deciding whether to sign a climate treaty.

Players: Nation A and Nation B.
Actions: Each country can choose to "Comply" with the treaty or "Cheat."
Payoffs: If both comply, the environment wins. If one complies and the other cheats, the cheater gets an economic boost while the complier bears all the costs.
Information: Each country must decide simultaneously, without knowing for sure if the other is secretly planning to cheat.

By mapping this out, we can predict exactly how these nations will behave.

What happens if one player has more information than the other?

That is an excellent question, and it gets right to the heart of what makes political and social interactions so fascinating—and sometimes so tense.

Information Asymmetry

When one player has more or better information than another, we call this . In economics and politics, this imbalance completely changes how players make decisions and how we model their behavior. To understand this, we contrast two types of environments:

Perfect Information: Every player knows the exact state of the world, the rules, and every single move that has been made up to that point. Think of Chess. Both players can see the entire board and know every past move.
Imperfect Information: Players do not know everything. This could mean they make decisions at the same time without knowing what the other chose (like our treaty example), or it could mean one player holds secret, private information that the other cannot see.

In politics, this happens constantly. Consider a state's military capability. A country might secretly develop a new defense system (private information). The rival nation has to make a strategic choice—whether to initiate a conflict—without knowing the true strength of its opponent. The player with more information can use this to bluff, while the player with less information must make decisions based on risk and probability.

How do players deal with this uncertainty in real life?

To deal with this uncertainty in real-life political and social arenas, players can't just throw up their hands; instead, they rely on strategic moves like signaling, screening, and reputation building to actively manage and reshape what other players know.

Leveling the Playing Field

When there is , players on both sides of the gap have strong incentives to change the balance of information. How they do this depends on whether they are the ones holding the secret information or the ones trying to uncover it.

Here is how those three main strategies play out in politics and sociology:

: This is an action taken by the informed player to credibly send a message about their true strength or intentions. To be credible, the signal must be costly—something a liar couldn't easily fake. In international relations, if a nation wants to signal a credible commitment to a defense treaty, simply saying "we will help you" is cheap. Instead, they might station their own troops on the ally's border. This is a highly costly, visible commitment that signals true intent.
Screening: This is an action taken by the uninformed player to force the informed player to reveal their private information. Think of how political parties vet potential candidates. They might subject them to intense background checks or force them to sign loyalty pledges, designing tests that only a truly aligned candidate would be willing to pass.
Reputation Building: Over repeated interactions, players establish a history to prove their reliability or toughness. A politician who consistently votes against their party's leadership builds a reputation as an independent maverick. Once established, this reputation acts as a powerful shortcut that tells other players exactly how they are likely to behave in future games.