Introduction to Game Theory and Design Basics
Here's something that has probably never occurred to you while rage-quitting a board game or grinding through one more dungeon run at midnight: you were thinking like a mathematician. Not a very happy one, maybe, but a mathematician nonetheless — weighing options, predicting what other players would do, deciding whether to cooperate or defect, calculating risk against reward. Games make us do this naturally, almost invisibly. And that's not an accident. That's what games are.
But before we go any further, it's worth asking a question that seems almost embarrassingly simple: what exactly is a game?
What Even Is a Game?
You already know, intuitively, that chess is a game. So is poker. So is basketball, Minecraft, Dungeons & Dragons, and the card game your family inevitably argues about over the holidays. But why are they games? What do a medieval strategy board, a casino table, and a sports arena have in common that makes us put them in the same category?
Here's a working definition we'll use throughout this course: a game is a system of rules that creates a space of meaningful choices, pursued toward a goal, with feedback that tells you how you're doing.
Let's unpack that slowly, because each word is doing real work.
A system of rules. Games have structure. They define what's possible and what isn't, what counts as winning and what counts as cheating. Without rules, you don't have a game — you just have people doing whatever they want. The rules aren't the boring part; they're the architecture that makes everything else possible.
A space of meaningful choices. This is the big one, and we'll come back to it in a moment. For now, notice that it says "meaningful" — not just "choices." More on why that distinction matters enormously.
Pursued toward a goal. Games have objectives. You're trying to reach somewhere, score something, survive longer, build more, accumulate more, eliminate the others. The goal is the horizon that gives your choices direction.
With feedback that tells you how you're doing. Games respond to you. The board state changes. Your score goes up. Your character takes damage. Something lets you know whether what you just did helped or hurt. That feedback loop is what makes games interactive rather than passive.
Notice what's conspicuously absent from that definition: any mention of fun, any mention of play, any mention of technology or components. A game, technically speaking, can be miserable. (Anyone who has played Monopoly with a die-hard capitalist knows this firsthand.) Fun is what we're designing toward — it's not baked into the definition. That separation matters, because it means fun is something we can actually study, design for, and improve. Which is exactly what this course is about.
Games vs. Play vs. Everything Else
"Okay," you might be thinking, "but what about playing in a sandbox? What about a two-year-old stacking blocks? What about watching a movie or reading a novel?" These are all forms of engagement, even joy — but they're not games, at least not in the sense we're using the word. Understanding why helps clarify what makes games special.
Play is broader than games. When a child improvises a story with action figures, when you doodle in the margins of a notebook, when you shoot free throws alone in a driveway with no score kept — that's play. It's exploratory, open-ended, self-directed. Play doesn't require rules, goals, or feedback systems. It's valuable, creative, and deeply human, but it's not a game. Play is the ocean; games are a particular kind of boat you can build on it.
Passive entertainment — film, TV, novels, music — involves a completely different relationship. A reader or viewer receives an experience crafted by someone else. Their emotional engagement can be intense, their attention fully captured, but they're not making decisions that change what happens. The story doesn't branch when you frown at a bad plot twist. The movie doesn't speed up because you're bored. You're a passenger, not a driver.
Games are different because they put you in the causal chain. Your choices change the state of the system. The outcome is, at least partly, contingent on what you decided to do. That's the property that creates genuine engagement, genuine tension, genuine stakes — even when the stakes are entirely fictional.
This also explains why interactive fiction and tabletop roleplaying games feel so different from reading a novel, even when they involve lots of reading. The moment your choices start mattering — the moment what you say to the goblin king changes what happens next — you've crossed from passive consumption into game territory.
The Secret Ingredient: Interesting Decisions
Back to that phrase from our definition: meaningful choices. Here's where most people's intuition about games goes subtly wrong, and correcting it will change how you see every game you ever play again.
Not all choices are interesting. Consider a simple example: Candyland, the classic children's board game. You draw a card. The card says to move to the purple square. You move to the purple square. Did you make a decision? Technically, no — there was nothing to decide. Candyland has zero player agency. It's a random walk through a colorful board, and the outcome is completely predetermined the moment you shuffle the deck. Kids enjoy it because they're learning turn-taking and the ritual of playing, but there's no strategic depth because there are no choices to make. It's closer to a very slow coin flip than it is to a game in our fullest sense.
Now compare that to a moment from Settlers of Catan (or its spiritual descendants). You have enough resources to either build a road that extends your network into contested territory or save those resources for a development card that might give you a knight — which you could use to block your rival's biggest hex. You can't do both. Your opponent is watching you. The settler you're racing hasn't moved yet this turn. What do you do?
That's an interesting decision. It has multiple viable options. It depends on information you have and information you're missing. The stakes are real within the game's logic. It connects to longer-term goals. It accounts for what other players might do. And crucially, there's no obviously correct answer — a good player can make a reasonable case for either choice depending on the broader situation.
Or think about poker. You have a mediocre hand. Your opponent just raised. Are they bluffing? Do they have something? What does your betting history suggest about your hand, from their perspective? Should you fold, call, or re-raise? Every piece of that analysis is about predicting another mind — a deeply human, deeply fascinating problem. The cards are almost secondary.
This is what we mean when we say games are structured systems for making interesting decisions. The rules and components aren't the point. They're the machinery that produces those moments of genuine decision-making — moments where you have to think, adapt, predict, and choose. When games work, those moments come reliably, and they feel meaningful. When games fail, it's often because the decisions dried up somehow: one strategy dominated all the others, or luck swamped skill entirely, or the "interesting" choice turned out to have an obvious right answer every time.
Everything in this course is, at some level, about understanding those moments and learning how to design them.
Two Lenses, One Coin
Here's the central argument this course is built on: game theory — the branch of mathematics and economics concerned with how rational agents make decisions under conditions of strategic interaction — tells us why players behave the way they do. Game design tells us what to do about it. They're not separate fields that happen to share a word. They're two sides of the same coin, and understanding both together is what separates games that feel alive from games that feel like homework.
Most courses don't make that connection. The game theory ones tend to stay safely inside economics textbooks, full of elegant diagrams and very few dragons. The game design ones often skip the intellectual foundations entirely and jump straight to "here's how to balance your numbers." We're going to do something different. Every time we dig into a theoretical idea — Nash equilibria, dominant strategies, cooperation problems — we're going to immediately ask: so what does this mean for your game? And every time we explore a design principle — feedback loops, player psychology, the feel of a well-tuned mechanic — we're going to trace it back to what we actually know about how people think and choose. Theory and practice, always in conversation.
Where This Course Takes You
By the end, you'll have two things. First, a genuinely useful mental model for understanding why players make the choices they make — which, as it happens, is also a surprisingly useful model for understanding why people make choices in the real world. Game theory has a lot to say about what happens beyond the table.
Second, and more concretely: a playable prototype of your own game. Not a concept document. Not a mood board. Something you can put in front of another human being and watch them actually play, which is simultaneously the most exciting and most terrifying thing a game designer gets to do.
Along the way, we'll move through the course in roughly three phases. First, the theory: game theory's big ideas, the logic of decisions, cooperation, competition, and why rational choices sometimes lead to terrible outcomes. Second, the craft: mechanics, loops, systems, balance, and what player psychology has to teach us about designing for fun. Third, the build: your game, your prototype, your playtest, your iteration. Each phase builds on the last. The theory won't feel abstract once you're using it to debug your own design.
A practical note on how to use this course: each section ends with an exercise. Do the exercises. Seriously. The ideas here are slippery when you're just reading them and suddenly obvious when you're trying to apply them to something real. You'll also be developing a running design project — a game concept that evolves section by section — so the work accumulates rather than starting fresh each time. Start simple. Scope small. The goal of your first game isn't to be great; it's to be real.
Fair warning: some of this is going to get weird before it gets clear. We'll encounter ideas that seem obvious until they suddenly aren't, strategies that seem rational until they're catastrophic, and design problems that seem simple until you realize they have seventeen moving parts. That's not a flaw in the material — that's exactly how it should be. Confusion is just curiosity that hasn't found its answer yet.
Grab your coffee. Let's play.
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