You can put away your board games; we’re not here to talk about that kind of game theory. In this guide game theory refers to mathematical models exploring the behavior of competing rational agents. Rational agents are persons or things who are intent on selecting the optimal outcome in a given scenario. Game theory can be a powerful analytical tool in situations wherein agents’ decisions influence others.’ Although initially applied to zero-sum games in economic theory, game theory has expanded to encompass all areas of the social sciences and beyond. Game on! Let’s learn about this idea.
By analyzing questions, you can see patterns emerge, patterns that will help you answer questions. Qwiz5 is all about those patterns. In each installment of Qwiz5, we take an answer line and look at its five most common clues. Here we explore five clues that will help you answer a tossup on game theory.
ZERO-SUM GAMES
Zero-Sum Games refer to situations (games, relationships, business deals, etc.) involving two parties in which one party’s gain is the other party’s loss. If one party loses and the other wins, the net gain from the interaction is zero. Determining the optimal method to solve a zero-sum game was the foundation of game theory.
JOHN VON NEUMANN
John (born János) was a Hungarian polymath whose work was essential to the development of game theory. Von Neumann’s wide-ranging intellectual interests included everything from quantum mechanics to economics, but he began to explore game theory in the late 1920s. Von Neumann proved the minimax theorem, a fundamental theorem of game theory, in 1928. He would go on to write Theory of Games and Economic Behavior with Oskar Morgenstern in 1944.
NASH EQUILIBRIUM
John Nash was another one of the founding fathers of game theory. His namesake Nash equilibrium is one of the most important principles of the discipline. In simple terms, Nash equilibrium can determine the optimal strategy in situations where players in a game are competing against each other with no incentive to change their initial strategy. So, in a state of Nash equilibrium no player has anything to gain by changing just their strategy if all other players’ strategies remain constant.
STAG HUNT
Not all game theory scenarios come from the 20th century. Eighteenth century French philosopher Jean-Jacques Rousseau formulated a problem known as the “stag hunt.” In this hypothetical situation a pair of hunters must make a choice: jointly hunt a stag or separately hunt two rabbits. Hunting a stag is tough work and requires a lot of cooperation, but the payoff is much bigger than catching a rabbit. Strategies for solving the problem are either risk dominant or payoff dominant, depending on what players prioritize. The stag hunt problem is often used to study social cooperation.
PRISONER’S DILEMMA
One of the most famous game theoretic problems is the prisoner’s dilemma. Two mathematicians from the RAND Corporation, Merrill Flood and Melvin Dresher, developed the foundation of the dilemma in the 1950s, but game theorist Alvin Tucker gave it its name. The typical prisoner’s dilemma is paradoxical in nature: each player acting in their own self-interest leads to a suboptimal outcome for the group. In the classic example, two prisoners are encouraged to betray the other. If both remain silent, they will have minimal jail time. If both betray each other (an action consistent with each prisoner acting in their personal interest) the total jail time for both is greater than in the first scenario.
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Quizbowl is about learning, not rote memorization, so we encourage you to use this as a springboard for further reading rather than as an endpoint. Here are a few things to check out:
Read this article to learn more about von Neumann’s many intellectual achievements.
Game theory doesn’t just apply to parlor games. It becomes even more important to understand when the stakes are higher - like nuclear weapons.
Nash Equilibrium can be a bit difficult to wrap your head around. This video shows a quick example of it.
If you think the prisoner’s dilemma is devious, just wait until you learn about the infinite prisoner's dilemma.
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