William Spaniel is a PhD student in political science at the University of Rochester, creator of the popular YouTube series Game Theory 101, and founder of gametheory101.com.

Learn to think on your feet! Follow along with this game theory series to better understand how people behave when confronted with a variety of decisions. This lesson will introduce you to William Spaniel’s series on game theory, and teach you what game theory is and why it’s important to study. For this series you’ll use basic algebra and a little introductory calculus.

What happens if two suspects are taken in for questioning on suspicion of robbery? If everyone is looking out for their own interests, the results might surprise you! Follow along with William Spaniel as he explains this classic game theory scenario. Learn how to decide which outcomes are most likely and what it means for a person to have a ‘strategically dominant strategy’.

Continue with the rest of this series to understand how people behave in increasingly complicated scenarios.

Learn to apply the Prisoner’s Dilemma strategy to a more complex game using a tactic called iterative elimination of strategically dominated strategies. In this lesson, William Spaniel will teach you how to identify scenarios that can be solved using this approach, and walk you through an example problem to get you on your way. Though not all games can be solved using this approach, it’s a good one to have in your game theory tool belt!

Inspired by the movie ‘A Beautiful Mind’? Learn what it really means to find a Nash equilibrium - or win-win situation - in this Game Theory 101 lesson. William Spaniel, author of ‘Game Theory 101: The Complete Textbook,’ will teach you how to set up and evaluate games and scenarios to find Nash equilibria - situations in which neither player benefits from switching their strategy.

Do you want to learn to more effectively cooperate and negotiate with coworkers or friends? Game theory isn’t just about winning or losing, it’s also about working together to achieve awesome goals. In this lesson in his game theory series, William Spaniel defines the Nash equilibrium, and then clarifies the formal definition with a real world example: traffic.

o you play logic games or like to strategize? For all you evil geniuses out there, this lesson from William Spaniel’s series on game theory will help you to solve for best responses based on the Nash equilibrium. Learn how to determine the best strategies for each player in a two-player game to arrive at four pure strategy Nash equilibria. Before long you’ll be ruling the world…or at least your opposition.

Do you know how to solve for outcomes in a two-player game, where there can only be one winner, and only one loser? In this lesson on mixed strategy Nash equilibrium from his series on game theory, William Spaniel explains how to solve a game with diametrically opposed interests (like soccer or football) when no pure strategy Nash equilibria exist.

How do you strategize or come to a decision when no pure Nash equilibria are present? Continuing his series on game theory, William Spaniel teaches you all about mixed strategy algorithms. Using a Zero-Sum mixed strategy game, William explains the math symbols and the algebra required to solve these equations, and then how to interpret the resulting probabilities. With the right information, you can make the decision that benefits you the most.

Have you ever lost points on a game theory assignment or test because you came to a slightly wrong conclusion? In this installment of his series on Game Theory, William Spaniel reveals one of the most frequent mistakes game theory students make: expressing mixed strategy Nash equilibria as decimals, not fractions. William demonstrates why 1/3 is not the same as .33, supporting his claim that when solving game theory equations, its always safe to stick with fractions.

You want to play golf, but your friend wants go surfing; you’d both rather be together than not. It is in your best interest to make the same decision, but you have a few options, and you have to decide without knowing your friend’s decision. Learn how to run a mixed strategy algorithm to determine if there is a mixed strategy equilibria. Once you can calculate the payoffs for a mixed strategy, you can make an educated decision and choose the option with the highest probability of success.

What would you do if you and your friend wanted to hang out together, but wanted to do completely different things? Now what if you had to decide what you would do without talking to your friend—but if you and your friend don’t pick the same thing, you don’t get to do anything at all, together or separately? Sound confusing? No longer! In this game theory lesson on calculating payoffs, you’ll learn how to calculate a payoff for a mixed strategy Nash equilibrium, for the best possible outcome.

If hitting a green or a blue button meant that you got cake, but hitting a red button meant you got Brussels sprouts, you’d always hit the green or the blue button, right? When you have multiple options, but certain options always yield better results than others, those others have been strictly dominated—meaning they aren’t as beneficial, so you can exclude them as options and make better decisions. Learn more about strictly dominant mixed strategies in this game theory lesson.

Let’s talk about international relations! In this introductory lesson, William Spaniel runs through the syllabus for his extensive course on international relations; from sovereignty and trade to war and terrorism, you’ll get a behind-the-scenes look at how nation states strategize to survive and prosper in the realm of global politics.

Who are the major actors in international relations? How did they come to exist? In this lesson by William Spaniel, learn how the concept of sovereignty — as outlined in the 1648 Treaty of Westphalia — has come to define the actors that take part in global politics. Through examples of sub-state conflicts, you’ll learn why sovereignty is so important today and how it is often violated.

Who is sovereign over sovereign states? Nobody! This lesson on international relations by William Spaniel demonstrates how, despite entities like the United Nations, sovereign states operate amongst each other in a state of complete anarchy. Learn why this is the case and how it does not spell complete chaos. Welcome to a world where anything can happen!

What does it mean for X to cause Y? While it may be easy to find a number of surface-level explanations — also known as proximate causes — for why an event has happened, it is more important to determine the underlying causes. Through understanding underlying causes, preventative courses of action for the future can be taken. Explore this concept, with examples, in this lesson on international relations by William Spaniel.

In the anarchic world of international relations, how can we predict and explain outcomes? In this lesson, William Spaniel applies game theory, a methodology created to study economic interdependence, to political science. With simple mathematical models, you too can turn assumptions into predictions of action in global politics.

Under what conditions can two parties play nice with one another? Answer this question and many more with this unit on conflict versus cooperation in international relations by William Spaniel. In this lesson, ground your conception of state conflicts with a practical example involving you, your roommate, and $20; also, find out what you’ll be learning over the course of the next six tutorials.

How can individually rational behavior lead to collectively bad outcomes? Here is your review of the prisoner’s dilemma, a classic game theory example involving two thieves who must decide whether or not to rat the other out. As an introduction to conflict and cooperation in international relations, the prisoner’s dilemma provides a practical grounding for the seemingly rational decisions that turn out to be costly in world politics.

Why did World War I start? Go above and beyond the stock answer involving the guy with a funny mustache named Franz Ferdinand. In this tutorial, William Spaniel applies the game matrix from “The Prisoner’s Dilemma” to early 20th century France and Germany to explain how the cult of the offensive turned a small politically-charged event into the first world war.

Why was it so hard to establish free trade? Though most of the world now functions via free trade agreements, there was a time (before World War II) that international trade was governed by exorbitant tariffs. In this lesson by William Spaniel, explore how the same principles used in the prisoner’s dilemma informed nations looking to keep domestic business from falling prey to cheaper foreign goods.

Why do states stockpile weapons and never use them? With the Cold War as a prime example, William Spaniel explores another way in which the prisoner’s dilemma of game theory finds its way into international relations. Learn how the concept of relative military power informs states’ decisions to spend billions of dollars on militarization, and get a preview of how states may finally settle on arms treaties.

Can future interactions inspire cooperation today? William Spaniel tackles the notion of repetitive international relations in this tutorial, using trade as an example. Discover why no matter how many interactions take place, as long as both sides know the date of a relations’ termination, cooperation can never take place. Again, the prisoner’s dilemma in game theory helps explain how aggressive logic contributes to negative results for both involved parties.

Learn how, once and for all, states apply game theory logic towards indefinite cooperation. Although it seems that the prisoner’s dilemma tends to incentivize aggressive and uncooperative action amongst states, you might be surprised to find that there is a scenario in which game theory actually lends itself towards international agreements. In this lesson, William Spaniel explains how states agree to free trade agreements and arms treaties using the grim trigger strategy.