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- Herausgeber: Icon Books
- Kategorie: Wissenschaft und neue Technologien
- Serie: Graphic Guides
- Sprache: Englisch
When should you adopt an aggressive business strategy? How do we make decisions when we don't have all the information? What makes international environmental cooperation possible? Game theory is the study of how we make a decision when the outcome of our moves depends on the decisions of someone else. Economists Ivan and Tuvana Pastine explain why, in these situations, we sometimes cooperate, sometimes clash, and sometimes act in a way that seems completely random. Stylishly brought to life by award-winning cartoonist Tom Humberstone, Game Theory will help readers understand behaviour in everything from our social lives to business, global politics to evolutionary biology. It provides a thrilling new perspective on the world we live in.
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Seitenzahl: 116
Veröffentlichungsjahr: 2017
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Contents
Cover
Title Page
Copyright
Why is it called “game theory”?
Working with models
“It’s a draw.”
Dealing with complexity: art and science
Rationality
Keynes’ Beauty Contest
Thaler’s Guessing Game
Problems with rationality and common knowledge of rationality
Booms and crashes: applying rationality to financial markets
Simultaneous-move games
Strategic form of the game
Payoffs
Nash equilibrium
Prisoners’ Dilemma
Pareto efficiency
Network engineering
The tragedy of the commons
Nuclear build-up
Cooperation
Education
Environmental policy and cooperation
Multiplicity of equilibria
Multiplicity of equilibria: Battle of the Sexes
Social norms
Coordination devices
Banking and expectations: bank runs
Mixed-strategy Nash equilibrium
The Currency Speculation Game
The Chicken Game
The Exit Game
Criticism and defence of mixed strategies
Tax evasion
Repeated interaction
At the end of the game
What if there is no definite last stage?
Prisoners’ Dilemma experiment
Evolutionary game theory
Hawk-Dove Game
The Hawk-Dove Game with small cost of conflict
The Hawk-Dove Game with large cost of conflict
Evolutionary stability as an equilibrium refinement
Sequential-move games
A dynamic Battle of Sexes Game
The extensive form of the game
Subgame perfection
Non-credible threats
Credit markets
Microcredit
Nuclear deterrence
Information problems
Asymmetric information
Asymmetric information and unemployment
More on asymmetric information
Signalling product quality
Warranties as a signalling device
Advertising as a signalling device
Religious ritual as a signalling device
Decision making in groups
Where we’ve come from …
… and where to go from here
About the Authors
Index
Published by Icon Books Ltd, Omnibus Business Centre, 39–41 North Road, London N7 9DP Email: [email protected]
ISBN: 978-178578-083-7
Text copyright © 2017 Icon Books Ltd
Illustrations copyright © 2017 Icon Books Ltd
The author and illustrator have asserted their moral rights
Editor: Kiera Jamison
No part of this book may be reproduced in any form, or by any means, without prior permission in writing from the publisher.
What is game theory?
Game theory is a set of tools used to help analyze situations where an individual’s best course of action depends on what others do or are expected to do. Game theory allows us to understand how people act in situations where they are interconnected.
Connections between people arise in all sorts of situations. Sometimes through cooperation with others we can achieve more than we can on our own. Other times conflict arises where an individual benefits at the expense of others. And in many situations, there are benefits to cooperation but elements of conflict also exist.
We only win when we work together, but right now everybody is trying to be the star.
Because game theory can help analyze any environment where a person’s best action depends on others’ behaviour, it has proven useful in a wide variety of fields.
In economics, the decisions of firms are affected by their expectations of a competitor’s choice of product, price and advertising.
In political science, a candidate’s policy platform is influenced by the policy announcements of their rival.
In biology, animals must compete for scarce resources, but can be hurt if they are too aggressive with the wrong rival.
In computer science, networked computers compete for bandwidth.
In sociology, public displays of non-conformist attitudes are influenced by others’ behaviour, which is shaped by social culture.
Darn! I was going to offer healthcare reform as the Key part of my policy platform. Guess I’ll have to come up with something else.
Game theory is useful whenever there is strategic interaction, whenever how well you do depends on the actions of others as well as your own choices. In these cases, people’s actions are influenced by their expectations of others’ actions.
Santa brought you a game. This isn’t a game! It has no strategic interaction. The other players moves don’t affect my best action. Global thermonuclear war is a game. In war. other players’ choices affect my best response, and my actions affect their behaviour. we should never have sotten him that Game Theory book!
Why is it called “game theory”?
Game theory is the study of strategic interaction. Strategic interaction is also the key element of most board games, which is where it gets its name. Your decision affects the other player’s actions and vice versa. Much of the jargon of game theory is borrowed directly from games. The decision makers are called players. Players make a move when they make a decision.
Sometimes I forget that I’m not playing chess.
Working with models
Real-world strategic interaction can be very complicated. In human interaction, for instance, it’s not just our decisions, but also our expressions, our tone of voice and our body language that influence others. People bring different histories and points of view to their dealings with others. This infinite variety can create very complex situations that are difficult to analyze.
We can circumvent this complexity by creating simplistic structures, called models. Models are simple enough to analyze but still capture some important feature of the real-world problem. A cleverly chosen simple model can help us learn something useful about the complex real-world problem.
what are you doing? Learning engineering.
The game of chess is useful for understanding the complexity that variation brings to playing (and to predicting) games and outcomes. There are well-defined rules in chess. There are a limited number of options in each move. Yet the complexity of the game is daunting even though it is much simpler than even the most basic human interaction.
There are 1040 sensible sequence of moves in a chess game – far more than there are grains of sand on Earth. So how on Earth can I predict what you’re soins to do next and plan my moves?
“It’s a draw.”
One feature of complex board games like chess is that the more skilled the players are, the more frequently the game ends with a draw. How can we explain this observation?
Since chess itself is too complex to fully analyze, let’s use a simple model that captures some of the important features of the chess game: noughts & crosses (tic-tac-toe). Both chess and noughts & crosses have well-defined boards and victory conditions. Players take turns making choices from a limited selection of possible moves.
There is quite a lot going on in chess that is not captured by noughts & crosses. But because the two games share some important features, noughts & crosses can help improve our understanding of why skilled players tend to end the game with a draw.
By playing tic-tac-toe I an learning about chess. Quit Stalling and move already!
Noughts & crosses is fun for small children. While the game between unskilled players tends to have a victor, after a bit of practice you quickly learn to reason via backward induction: you can figure out your opponent’s response to your possible actions and take that into consideration before making your own move.
Once players learn to reason via backward induction, all noughts & crosses games are likely to end in a draw. In this way, noughts & crosses works as a simple model of chess, in which there are far more possible moves, but which, when played between skilled players is also likely to end in a draw.
Time to move on to something a bit more complicated.
Dealing with complexity: art and science
The primary concern of game theory is not board games like chess. Rather, its aim is to improve our understanding of interactions between people, companies, countries, animals, etc., when the actual problems are too complex to fully understand.
To do this in game theory we create very simplified models, which are called games. The creation of a useful model is both a science and an art. A good model is simple enough to allow us to fully understand the incentives motivating players. At the same time, it must capture important elements of reality, which involves creative insight and judgement to determine which elements are most relevant.
There is not one true model of any situation. There can be many models, each of which highlights a different aspect of the actual strategic interaction.
Rationality
Game theory usually assumes rationality and common knowledge of rationality. Rationality refers to players understanding the setup of the game and exercising the ability to reason.
Common knowledge of rationality is a more subtle requirement. Not only do we both have to be rational, but I have to know that you are rational. I also need a second level of knowledge: I have to know that you know that I am rational. I need a third level of knowledge as well: I have to know that you know that I know that you know I am rational. And so on to deeper and deeper levels. Common knowledge of rationality requires that we are able to continue this chain of knowledge indefinitely.
I Know that you Know that I Know you are rational. I Know that.
Keynes’ Beauty Contest
The requirements for common knowledge of rationality are confusing to read. But worse, they might well break down in reality, especially in games with many players. A classic example is Keynes’ Beauty Contest, in which English economist John Maynard Keynes (1883–1946) likens investment in financial markets to a newspaper competition in which readers have to choose the “prettiest face”; the readers who choose the most frequently chosen face win.
‘It is not a case of choosing those which, to the best of one’s judgement, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest… we devote our intelligences to anticipating what average opinion expects the average opinion to be.’
At first glance, Keynes’ Beauty Contest has very little to do with financial markets: there are no prices, and there are no buyers or sellers. But they have one crucial feature in common. Success in financial markets depends on being one step ahead of the crowd. If you can predict the behaviour of the average investor, you can make a killing. Likewise in Keynes’ Beauty Contest, if you can predict the average choice of newspaper readers, you can win the contest.
I think brunettes are prettier, but most people prefer blondes, so I think the blonde will be the most popular. I choose the blonde. This stock is too expensive. But I’ll buy it anyway because I think others will be buying it, so the price will go up even further.
Thaler’s Guessing Game
In 1997 the American behavioural economist Richard Thaler (b. 1945) ran an experiment in the Financial Times a Guessing Game which was a version of Keynes’ Beauty Contest.
GUESS THE NUMBER! Readers pick a number between zero and 100. The winner is the contestant with the number closest to 2/3 of the average of all numbers entered in the contest.
Which number would you pick?
In Thaler’s Financial Times experiment, the newspaper received more than a thousand entries. The entry 33 was the most frequently picked number, followed by the number 22. This suggests that many people reasoned one step and so chose 33. But many others thought that other readers would stop there and tried to be one step ahead of them by choosing 22 (which is 2/3 of 33).
If you believe that others will stop at the first step of reasoning, it is rational -for you to stop at the second step.
However, if there is common knowledge of rationality, you know that others will not stop at the first step, so you can continue this iterative reasoning forever – a process of reasoning that involves repetition of the same process, taking the result from one round as a starting point for the next.
Game theorists solve the Guessing Game in a similar fashion using iterative elimination of dominated strategies.
Remember that you’re looking for 2/3 of the average number entered into the contest. If all contestants were to pick the highest permissible number, 100, the average would be 100. Hence, no matter what one expects the average to be, it makes no sense to ever guess a number greater than 2/3 of 100, which is 67.
In other words, any strategy with a guess greater than 67 is dominated by 67. A strategy is dominated if it (in this case, a guess higher than 67) is worse than another strategy (guessing 67) regardless of what other players do. Hence, even if no one else is rational, all strategies with a guess greater than 67 can be eliminated.
If everyone else is rational, then each player can reason that no one would guess a number higher than 67. Hence, guesses above 45 (which is the closest integer to 2/3 of 67) are also eliminated. And because each player knows that the others know that everyone is rational they can each be certain that nobody else would choose a number greater than 45, and so they will not choose a number greater than 30 which is 2/3 of 45.
In the Guessing Game, iterative reasoning leads to smaller and smaller numbers, until all numbers above zero have been eliminated as dominated strategies. So. rational people with common Knowledge of rationality would pick zero.
Problems with rationality and common knowledge of rationality
Zero, however, was not the winning number in the Financial Times experiment. The average number came out to 19 and so the winner had the entry 13.
The winning number was much higher than what game theorists would have predicted. Where does game theory go wrong? Does game theory not have any predictive power?
In this case, the assumptions of rationality and common knowledge of rationality are not satisfied. For instance, many contestants picked the number 100, which is not rational. Even if one were to mistakenly expect everybody to pick 100, the optimal response would be 67. These contestants either did not fully understand the rules of the game or they were not able to calculate 2/3 of 100.
