Pick the price that maximizes your revenue.

That’s it. That’s all. Just pick the price that maximizes the total cash your book brings in. Picking anything else is stupid.

This is a tall order. It’s not immediately clear which price will generate the most money for you. Amazon offers 35% royalties on books between $0.99 and $2.98. Anything between $2.99 and $9.99 nets 70% (minus a usually negligible data transfer fee). So a $0.99 book needs to sell between five and six as many books as a $2.99 book to keep pace. Whether the higher demand from the cheaper price justifies selling at $0.99 remains to be seen and probably varies from book to book and genre to genre. An author might have to experiment with different price points before settling on the right one for him.

An author must also weigh the value of sacrificing extra revenue from a single book to generate additional revenue for rest of the author’s library. For example, the author of a trilogy might want to sell the first book at $0.99 and the other two books at $2.99. The cheap introduction brings more readers into the series, which in turn will lead to additional sales of the more expensive selections. I run a similar strategy with my game theory textbook, selling the first chapter at $0.99 and a larger version at $2.99.

Some people’s pricing strategy baffles me, however. Some people refuse to price books at lower prices because they do not feel it adequately reflects the amount of work the author put into the book. Absolute nonsense! The time you spend writing a book is a completely sunk cost once you are done. Placing a book at $4.99 because you think that is the value of the book is beyond ridiculous. The market determines the appropriate price. If selling at $0.99 or $2.99 brings in more revenue, your resistance to lowering your price only makes it more difficult for you to pay your rent. It also leads to fewer people buying into your brand and therefore fewer sales of your other books. These authors need to get over themselves.

Just pick the price that maximizes your revenue. It’s that easy…at least in theory.

My larger textbook—Game Theory 101: The Basics and Extensive Form—has been doing quite well. This month, it has averaged a little more than ten sales per day. I know that might not sound a lot, but it projects to more than 3500 sales over the course of a year, or $5600. That is a lot of money for a graduate student living off of a small stipend. It’s also a lot for an academic book, most of which will get about 200 sales over their lifetime.

However, my book received its first review yesterday. It was not so good:

I regret this purchase, even at only $2.99. This is way below “101″ level. This is about a 6th grade level…[i]f you are considering this product, you are better off reading the Wikipedia articles on Game Theory – it will be free and much more productive.

Needless to say, he gave me 1 star. Now, whenever someone searches for game theory on Amazon, they will see my book is worth one measly star.

How does that impact a seller? Despite averaging more than ten copies per day this month, I have not sold a single one since that time. Yikes.

The part of the review that I put above—the book is very basic. (There is more to the review that I believe is incorrect, but I excluded it from above to keep this conversation focused.) But that’s the point. I want the book to be simple. Game theory should be simple. There should be no magic or hand waving. The number one complain I receive from students taking game theory is that they have no idea how to solve games despite attending every lecture, section, and office hour they could. That’s why I created my video series, which eventually evolved into the textbook.

But his suggestion to read Wikipedia instead is ridiculous. Go read the Wikipedia page on how to solve for mixed strategy Nash equilibrium. Then try to solve the game in this video. Best of luck to you.

My personal feelings aside, consider an objective metric of the quality of a book: the rate of return. Amazon gives you a seven day window to return a Kindle book that does not meet your expectations. My small textbook has a rating of 5 stars (from a single, trollish review). In the last two months, it has a return rate of 0.69%, meaning a little more than 1 in 150 of these books gets returned. (For perspective, I’ve heard anything less than 5% is good, so I’m well below that mark here.)

The bigger textbook? The one with a 1-star review? Zero returns in the last two months. None. Buyers, it appears, like the larger textbook better. Yet it appears from the reviews that the opposite is true.

Edit: Looking back, I noticed I only calculated this from US sales. There was a single return of the bigger textbook from Amazon UK. So the return rate wasn’t exactly zero for the world, but it was darn close.

I’m curious why Amazon does not show the return rate for each book. Writing a review is time consuming, so you might get one review for every couple thousand books you sell. Consequently, the reviews don’t really tell you what the average person thinks of the book. Returning a book, on the other hand, is not costly, since it puts money back in the customer’s pocket. It is a better metric of a book’s value to its customers.

Anyway, hopefully my sales will return. In the meantime, if you have read Game Theory 101: The Basics and Extensive Form, please write a review. =) Whether you think it is five stars or one, at least the review will better reflect what everyone thinks as a whole.

Let me know if you see any problems.

Civil wars almost always end when one side completely defeats the other militarily. This process usually takes a long time. Libya will likely fit the pattern, especially since Gaddafi cannot use his airforce due to the no-fly zone, while the rebels do not really have one. Make no mistake about it: we will be enforcing the no-fly zone for a while.

I’ve been thinking about this Iran problem for a while now. Naturally, I drew up a model for the interaction. My first manuscript showed that modeling power shifts exogenously is misguided–it is like saying “guns grow on trees.” But there is another awful assumption that my last model and all other models on the subject use. We model shifting power as though it is free–as though, once again, guns grew on trees.

This could not be further from the truth. Since the Iran issue involves nuclear weapons, let’s start there. Try guessing how much the United States has spent on its program. Statistics like these are hard to come by, but I found one study that took a comprehensive look at America’s expenditures. And you are going to have to think big. Really, really big. Like $7+ trillion in 1996 dollars big.

So if states have to pay that much money to shift power, why the heck are they doing it at all? Well, the obvious answer is that they can get the cost back at the bargaining table by coercing the opponent to make concessions. Put differently, weapons are an extortionate investment in the future.

My model shows that this is not the full story. There are four types of equlibria. When the power shift is too great, the rising state refuses to build out of fear of preventive war–this is the same finding I had in my last paper. When the cost of building is too great, the rising state refuses to shift power because it won’t be able to recoup its costs.

Between those two, things get interesting. If the declining state is really impatient, it can leverage the rising state’s future power against it. In other words, the declining state offers the rising state a minimal amount today, and the rising state accepts anyway, knowing it will make up for the lowball offer later, when the rising state will have to make great concessions. But as I explain in the paper, I feel it is unrealistic to believe that a declining state would have such a great discount factor.

In the last equilibrium, the declining state makes a small amount of concessions to the rising state immediately. The rising state could build anyway, but the additional concessions it would earn are not worth the cost of building. Meanwhile, the declining state benefits because it keeps all of the extra concessions it would have made had it forced the rising state to build. Essentially, I show that the two sides can divide the surplus that comes from not building weapons in a credible manner over the course of time.

There is a big implication here with Iran. Many claim we will not be able to deter Iran from building a nuclear arsenal no matter what we do. Perhaps this is the case. Feel free to continue thinking that; just know that you are really claiming that Iran is irrational. But if they are rational, if we offer them enough, we will appease them, and we’ll come out of the deal in better position than had we forced them to build.

Interested in formal models of inter-state conflict.

You may know me from my textbook (Game Theory 101: The Basics), my other website (gametheory101.com), my game theory videos on YouTube, Freakonomics, or my quant/formal work on applied games.

Email me at williamspaniel@gmail.com or following me on Twitter @gametheory101.