Crack all plc hmi passwords. Recently an economics exam question from the University of Maryland went viral on Twitter.
WHAT KIND OF PROFESSOR DOES THIS pic.twitter.com/ACtQ0FCwRm
— name (@shaunhin) July 1, 2015
Here’s the question in written as plain text.
Here you have the opportunity to earn some extra credit on your final paper grade. Select whether you want 2 points or 6 points added onto your final paper grade. But there’s a small catch: if more than 10% of the class selects 6 points, then no one gets any points. Your responses will be anonymous to the rest of the class, only I will see the responses.
- 2 points
- 6 points
How would you answer?
Below I’ll give the mathematical way to tackle this problem using game theory.
Video
I’ve prepared a brief video that explains the logical choice.
I’ve explained all the details of the video and more in the discussion below.
Brief intro to game theory
In decision theory, your decision to buy an extended warranty or lease a car is an individual choice. You weigh the costs and benefits of the decision and choose whether to do it.
Most decisions in life are not so simple. They also depend on what others will do. Your choice to buy Apple products depends on whether others will buy them too, which will lead to a larger market for accessories, developers making better apps, and hotels or cars having iPhone compatible chargers. You might actually prefer Android devices but you find Apple products are a better decision overall for this reason. Your choice depends on what you do as well as what others do.
Game theory studies such situations of interdependent decision-making. Game theory helps you make the right decisions, it helps you identify the strategic incentives in a game, and ultimately that can help you design better mechanisms so everyone can benefit.
The Nash equilibrium is a the most common game solution. It happens when each person is making the best choice relative to what everyone else is doing. No one can individually change and profit. So let’s return to the exam question.
Your logical thought process on the test
Many people think, “I’ll just take 2 because if everyone does this we all get 2.” But that’s not really a careful analysis of the game. You have to think about your best choice relative to what others can do. If everyone else is picking 2, why wouldn’t you pick 6 and get extra points?
So let’s analyze the problem carefully. We’ll consider your choices and they relate to what others might do.
You have two choices: you can pick 2 or you can pick 6.
The result depends on what other people do. The crucial detail is how many people are picking 6. So let’s categorize the actions of everyone else in that regard. There are essentially two main ways that everyone else can pick.
A) More than 10% pick 6.
B) Less than 10% pick 6 (and your choice doesn’t bump it above 10%).
B) Less than 10% pick 6 (and your choice doesn’t bump it above 10%).
In option A), too many people have picked 6, so everyone is getting 0. You will get 0 regardless of whether you pick 2 or 6.
In option B), if you pick 6 then you will get 6 points. This is clearly the right choice as you will get more points.
In other words, in options A) and B) it is clearly smart to pick 6.
If everyone thinks this way, then everyone will pick 6, and everyone will end up with 0 points. It feels like individual greed leads the group to a bad outcome, which is why people feel the question is evil. I’ll get to the moral part in a bit. But for now, let’s summarize that this is one Nash equilibrium: each person picks 6 and everyone gets 0.
Another possible outcome
There is one more way this game can play out (in pure strategies). Suppose that just the right amount of people pick 6:
C) Exactly 10% pick 6 (or as many as possible without exceeding).
For example, in a class of 10, suppose one person picks 6 and everyone else picks 2. The person who gets 6 is happy to get 6. And each person who picks 2 is content with this outcome: if any person changes to 6, then that person (and everyone) ends up with 0 instead.
In other words, if the maximum amount of people pick 6 and everyone else picks 2, then no one can individually do any better given what others are doing. This is also a Nash equilibrium.
In summary, there are two types of pure strategy Nash equilibrium: one where everyone picks 6, and another “Goldilocks” solution where exactly the maximum number pick 6 and everyone else picks 2.
The second category is a kind of magical solution because it is hard to imagine people exactly coordinating with no communication.
Relative payoffs
The above analysis assumes that each person wants to maximize points. This would be a correct assumption if exams were based on absolute point threshold: say 90 points for an A grade, 80 points for a B grade, etc.
College exams are typically graded on a curve. Your grade is dependent on how well you do relative to others. So it might be that a 70 percent gets you an A grade because everyone did worse.
A strategic student should then maximize relative points–the number of points you would earn more than others. If everyone gets 2 more points, then no one is relatively better. So let’s solve the game in terms of relative payoffs.
You still have two choices to consider: you can pick 2 or you can pick 6. But now the game has the following payout structure.
You can pick 2 or 6.
If everyone picks 2, then everyone gets 0 extra points.
If less than 10 percent pick 6, then the people who picked 2 get 0 extra points, and the people who picked 6 get 4 extra points.
If more than 10 percent pick 6, then everyone gets 0 extra points.
If you pick 2, you are guaranteed to get 0 extra points. If you pick 6, there is a small chance you might get 4 extra points. In game theory jargon, 6 is a weakly dominant strategy.
When you have a weakly dominant strategy, you should play it.
So everyone picks 6, and the Nash equilibrium is everyone gets 0 extra points.
What actually happened
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The professor explained to the Baltimore Sun that more than 10 percent of students picked 6, so no one got extra points.
The situation is an example of a social dilemma: while there is a chance for everyone to possibly benefit with more points, the exact nature of the game gives each person an incentive to pick 6 points, which is ruinous for everyone in aggregate.
The temptation that spoils it for everyone is why some people call this game a tragedy of the commons.
(It’s more accurately an example of a volunteer’s dilemma in which some people have to sacrifice so others can benefit).
I used to wonder why more people don’t pick 2 so that everyone can benefit. But I do not feel that way any more. I think you should not feel bad about picking 6, and the problem is the game is rigged against what is individually sensible.
Music Theory Answer Key
In real life, the powers that be will tell you to pick 2 while they pick 6. And if you try and change things, you will face resistance from other 2’s that think you are spoiling things.
The game theory analysis proves that 6 is the logical choice. I’d say the real tragedy, if there is any, is that it’s not easy to convince people to do what’s logical.
Update: July 20
The professor compared the problem to a tragedy of the commons. I highly disagree with this characterization of the problem for the reasons outlined in this post. The article is worth reading as it covers other examples of the tragedy of the commons.
Sources
Tweet of exam question
Tweet of exam question
Professor Dylan Selterman: Twitter and homepage
Tadelis Game Theory Solutions Pdf
This book is a selection of the best articles from Game Theory Tuesdays, a column from the blog Mind Your Decisions. Articles from Game Theory Tuesdays have been referenced in The Freakonomics Blog, Yahoo Finance, and CNN.com. Game theory is the study of interactive decision making--that is, in situations where each person's action affects the outcome for the whole group. Game theory is a beautiful subject and this book will teach you how to understand the theory and practically implement solutions through a series of stories and the aid of over 30 illustrations. This book has two primary objectives. (1) To help you recognize strategic games, like the Prisoner's Dilemma, Bertrand Duopoly, Hotelling's Game, the Game of Chicken, and Mutually Assured Destruction. (2) To show you how to make better decisions and change the game, a powerful concept that can transform no-win situations into mutually beneficial outcomes. You'll learn how to negotiate better by making your threats credible, sometimes limiting options or burning bridges, and thinking about new ways to create better outcomes. As these goals indicate, game theory is about more than board games and gambling. It all seems so simple, and yet that definition belies the complexity of game theory. While it may only take seconds to get a sense of game theory, it takes a lifetime to appreciate and master it. This book will get you started.
Book Name: Game Theory: An Introduction
Author: Steven Tadelis
ISBN-10: 0691129088
Year: 2013
Pages: 417
Language: English
File size: 3.65 MB
File format: PDF
Author: Steven Tadelis
ISBN-10: 0691129088
Year: 2013
Pages: 417
Language: English
File size: 3.65 MB
File format: PDF
Game Theory: An Introduction Book Description:
This comprehensive textbook introduces readers to the principal ideas and applications of game theory, in a style that combines rigor with accessibility. Steven Tadelis begins with a concise description of rational decision making, and goes on to discuss strategic and extensive form games with complete information, Bayesian games, and extensive form games with imperfect information. He covers a host of topics, including multistage and repeated games, bargaining theory, auctions, rent-seeking games, mechanism design, signaling games, reputation building, and information transmission games. Unlike other books on game theory, this one begins with the idea of rationality and explores its implications for multiperson decision problems through concepts like dominated strategies and rationalizability. Only then does it present the subject of Nash equilibrium and its derivatives.
Game Theory: An Introduction is the ideal textbook for advanced undergraduate and beginning graduate students. Throughout, concepts and methods are explained using real-world examples backed by precise analytic material. Corel paintshop pro x7 free download. The book features many important applications to economics and political science, as well as numerous exercises that focus on how to formalize informal situations and then analyze them.
Read Theory Answers
* Introduces the core ideas and applications of game theory
* Covers static and dynamic games, with complete and incomplete information
* Features a variety of examples, applications, and exercises
* Topics include repeated games, bargaining, auctions, signaling, reputation, and information transmission
* Ideal for advanced undergraduate and beginning graduate students
* Complete solutions available to teachers and selected solutions available to students
* Covers static and dynamic games, with complete and incomplete information
* Features a variety of examples, applications, and exercises
* Topics include repeated games, bargaining, auctions, signaling, reputation, and information transmission
* Ideal for advanced undergraduate and beginning graduate students
* Complete solutions available to teachers and selected solutions available to students