Copyright: 2007
Publisher: Oxford University Press
ISBN: 978-0-19-921846-2
While true to part of its sub-title (it is definitely short) this book leaves somewhat to be desired if you are looking for an "Introduction". Binmore is an expert in using Game Theory so in his book by that title, he definitely gets into the meat of actually applying game theory to real life. He talks about biological evolution, public airwave auctions and election politics. Unfortunately he dives into game theory far too fast and too deep for this to be a good introduction. A more appropriate title would have been "Game Theory Applied: A Very Short but Broad Overview."
Utility and Consistency
Early in the book, Binmore discusses briefly the concepts of utility. He makes and interesting observation in that acting consistenly is similar to acting to maximize the value of something. In other words, if we observe consistent behavior in someone, we know that they are trying to maximize the value of something, even if we don't know the specific something being referenced.
This concept is helpful in user interaction design for software developers. We might not always know what a user values the most, but observing consistent behavior tells us they are trying to maximize something. This week I ran across this quote in a slide deck: "The behavior you are seeing is the behavior you've designed for. (Whether intended or not)." The slide deck was titled Designing for Social Traction by Joshua Porter. The idea here is that if we observe behavior in our users that we don't like, chances are they are simply trying to maximize some level of utility of which we aren't aware. Our job as human computer interaction engineers is to figure out what the user really values and design with that in mind.
Good Samaritan or Bad Neighbor?
We have all read or heard about the tragedy of someone being mugged in a public place and yet no one offering to help or even call the police. Binmore talks about this unsettling behavior in humans and points out that it is perfectly rational and logical for this to happen. To understand you need to think about the game in terms of numbers. We will use "utils" to refer to something for which you have a preference, it might be time, it might be money, it might just be pleasure.
Let's have a group of people around someone in trouble. If the person is helped by someone everyone get 10 utils each. If no one helps the person no one gets utils. The problem is, you lose 1 util if you are the one to help. Now logically if everyone helps. your best strategy is not to help since you will get 10 utils and lose none. If you understand Nash equilibriums (which Binmore does explain briefly!) then you understand that there is 1 chance in 10 that no one else offers to help. We know this because we are indifferent between helping and not helping.
So if there are only 2 players, in order to have a 1/10 probability of the other person helping, each has a 9/10 probability of being the one to help. So only 1 time out of a 100 does the cry for help get ignored. Unfortunately, as you add players to the game, the probability of any one player helping goes down (in order to keep the chance of someone else helping at 1/10). Thus is makes perfect sense that when a large crowd hears a cry for help, no one person has a great chance of helping because they all assume someone else will help.
Does this make us all bad neighbors? No, but the numbers are certainly very interesting. I think the very fact of knowing these facts can add some utility to the act of helping someone in a large crowd. The mere holding of knowledge can dislodge the unfortunately equilibrium by creating new utility values in one or a few of the players.
What Doesn't Happen Is Important
When you get deeper into game theory, you begin to deal with iterative games and you see paths in games that are never taken. We know this to be true in table games such as checkers. There are moves that people simply don't take. However, are these moves not taken important in any way? Should we take into consideration behaviors that we never expect to see?
An event that isn't going to happen is a counterfactual. Sometimes we like to think that these counterfactual events aren't important because they are simply hypotheticals. Interestingly, Binmore argues that these sub-games that will never be reached are important precisely because they will never be reached.
To understand this, you need to understand that there is a reason these sub-games will never happen. The consequences of reaching them would be suboptimal for one or both of the players thus that part of the decision tree will forever remain unused. Understanding what makes these decisions suboptimal can be important when designing future decision trees.
Often in developing software, we provide the user with a decision tree as they process some task. If we come across a decision branch that is seldom if ever used, we can use our understanding of that to move that branch somewhere else in the tree, potentially shortening the decision tree for the user. Anything we can do to make more efficient use of the users time is generally a good thing.
Point of View
We are used to having our own point of view and dealing with others with potentially different points of view. Game theory takes a persons point of view into account using the notion of focal points or framing. Often it is necessary to understand the framing problem when conducting real games using real subjects.
For instance, in a theoretical game, you might set up a scenario where two people are driving towards each other. The game says both must simultaneously choose whether to go to the right or to the left. What is the optimal or logical choice? Logically it's a coin toss. If you were to conduct this game in real life in the U.S. you would find a great number of the players both choose "right". The same test conducted in the U.K. would have very different results! This is because from the point of view of U.S. drivers, "right" makes logical sense and in the U.K. "left" is the obvious choice.
When designing an interface for a user, the developer cannot design in a bubble. Nor can a developer design from his or her own point of view. Rather it is important to understand the focal point of the end user and use that to frame the design of the interface.
In addition, there are a number of designers who argue for using hard rules such as Fitts' law to design their interface. If the convention for the user is the go to the lower left hand corner to start a program, then arguing that the upper right hand corner is a better location for the "Start" button is going to miss the point.
Incentives Work... (but not always how we want them to!)
Binmore does a good job of applying Game Theory to the real world and one area he addresses is mechanism design. Mechanism design is solving the problem of finding the right combination of rules and incentives to accomplish your goals. Often we design incentive systems and only take into account one Nash equilibrium that we are striving to reach. Sometimes we hit the mark but there are other times when the incentives lead to a different equilibrium than the one we envisioned.
This happened all the time when I was at FedEx. Upper management was constantly tweaking the rules to try to incentivize the couriers to perform their jobs a certain way. It seemed like every time they made a change to the rules, some unintended behavior would result and after a certain amount of denial, the management would once again go to the drawing board to rework the rules yet again. This led to a certain amount of cynicism among the couriers and a common saying became "tell us what the rules are today and we will beat you at your own game... again."
Conclusion
The book is quite short. Even though it is 174 pages, the book is very small in size so the reading is quick. If you have never read any game theory or taken any classes using it, this book is not a good one for you. Binmore consistenly assumes you already know what the "matching pennies" game is or what is meant by minimax. He spends an unfortunate amount of time nitpicking some commonly accepted notions of game theory, probably because he is somewhat of an expert and feels the need to make his views known. He also goes into a number of applications that are only going to be interesting if you are already hard core into game theory or are heavily into a particular field (biology being one of them.) All in all the book is a good quick read if you want a refresher on some game theory or want to see some very quick practical applications.