
The same textbook that sells for $100 in America might sell for $10 abroad. Several years ago, a student profited by importing cheap textbooks from Thailand and re-selling them in America, earning over $1 million.
Was what the student did legal? Publishing companies argued it was not, and they sued him to end the practice. At first the publishing companies won. But the student appealed and a legal battle ensued until the case reached the U.S. Supreme Court.
In March, the Supreme Court ruled in favor of the student, saying that resale was legal as part of the “first sale doctrine,” the idea that a customer has the right to re-sell and distribute a legally purchased trademarked product.
The ruling has put publishing and media companies in a bind. Before they could control price in markets separately. But now it seems they will have to consider a more uniform price across markets, lest someone else profit through resale.
There is a trade-off to raising and lowering prices across the board. If they maintain high prices everywhere, they lose sales abroad for people who cannot afford them, or who might decide to buy cheap pirated copies. On the other hand, if the publishers lower their prices, they obviously lose out in the American market.
How might this game play out?
Game theory suggests textbook publishers have entered a potentially wild and chaotic game. A simple model explained below indicates the game might in fact have no equilibrium strategy.
A simple model of textbook competition
Consider two companies X and Y that sell the same product in three markets A, B, and C. Suppose company X has a monopoly in A, company Y in C, and the two compete in market B. The situation looks like this.
Assuming each company can supply as much product as needed, how will this game play out?
The answer is easy to deduce. Since company X has a monopoly in market A, it will charge a monopoly profit-maximizing price. Similarly, company Y will charge a monopoly price in market C.
The interesting case is market B where both companies compete on price. If customers care only about price, then the game is one of Bertrand competition. The strategy is that each company will want to undercut the other in a price war that leads to the competitive market price.
The game results in two different prices: a monopoly price in A and C, and a much lower competitive price in B.
Now imagine that people in markets A and C realize that market B has a much lower price. How will that change the game? Very likely the good will get bought cheaply in market B and imported to markets A and C, driving the price down.
The threat of arbitrage changes the game for companies X and Y. Consider the extreme case that the threat of resale means the companies can no longer effectively price differently in their markets. In other words, assume that each company has to sell for a single price in the two markets it serves.
What is the Nash equilibrium of this game?
To be precise, assume each market is the same size (normalized to 1). Also assume that product can be shipped from market B to market A or market C, but that trade is banned between markets A and C.
Further, without loss of generality, let the price charged be between 0 and 1, and let the product have a marginal cost of 0. Assume that market B is a Bertrand competition: consumers opt for the lower price, and if the price is the same, the market is split.
(Reference: this game is borrowed from Algorithmic Game Theory edited by Noam Nisan, et al. See section 1.5 “Games with No Nash Equilibrium”)
Solving the game?
Let’s say that company X charges a price of 1 in markets A and B. If company Y also charges 1 in each market it serves, then here is how the competition will play out.
Company X gets all of market A, which is a profit of 1, and it will split market B with its competitor to earn 0.5. Thus, company A nets 1.5. Company Y profits exactly the same.
Is this an equilibrium? Definitely not. Company Y realizes it can earn more by undercutting the price. If company Y charges 0.99, then it will still earn nearly the same in its monopoly market. But at the same time, its price is lower in market B and so it will capture the entire market. Company Y will profit 0.99 in market B, and so its total profits become 1.98.
Company X, of course, will not stand idle and be undercut. It will respond with a price of 0.98, which allows it to capture market B with minimal loss in its monopoly market. Its total profits will rise to 1.96.
In normal Bertrand competition, the game proceeds with each company undercutting the other. But this is not a normal Bertrand competition!
Things get interesting when one company charges a price of 0.5. What is the best thing for the other company to do? One choice is to undercut to a price of 0.49. That will yield a profit of 0.98. But that choice doesn’t make sense. Instead, the company could respond by raising its price to 1. Why is that? Because the company can earn a monopoly price in its home market!
So now one company is charging a price of 1 to earn a profit of 1. The other company realizes it is foolishly charging 0.5 earning a modest profit of 1. Instead, it can best respond by raising its price to 0.99, netting a profit of 1.98!
Formally, the best response function is:
–if the other company charges a price p between 0.5 and 1, then charge slightly less than p
–if the other company charges a price p less than or equal to 0.5 , then charge the maximum price of 1
You can see the trouble. For any price a competitor charges between 1 and 0.5, the strategy is to undercut. But once the competitor is charging 0.5, the best response is to raise the price to 1.
The result is the game has no pure strategy Nash equilibrium. The two companies will endlessly battle on price and never be satisfied.
(The source states the game has no mixed strategy equilibrium either, but the proof of that is left to the reader.)
What does this mean for textbook publishers?
The answer of “there is no equilibrium” is not an assuring one for the marketplace. Publishers have to set some price and compete, but any strategy they choose can be exploited by a competitor.
How might the game play out? My suspicion is that publishers will probably maintain high prices in the short run. They might lose out on foreign sales, but they can at least maintain profits at home.
In the long run they will have to find other ways to price discriminate, perhaps by setting different subscription prices for a multimedia textbook or coming up with a different kind of game-changing move.
Even though you can share messages, pictures and videos in multiple ways like instant messaging, social networking sites and email online, all these services come with issues like requiring a login or having a client already installed.
Socket.im is a new tool which allows anyone to share stuff between multiple users without any hassle. All you need to do is type socket.im/something in your browser and the website creates a socket for you. At present one can only send messages and links but in the future one will be able to send images, videos and pretty much any type of file. The person who needs to receive the files just needs to go to the socket link and the messages will begin appearing in real time. Nothing is stored on the server.
One can also choose to remain anonymous or set a nick name so that people know who is sending a message.
This is different from instant messaging as one does not require a login for socket.im. So one can remain anonymous if you wish. It is also intended to be more real-time sharing platform.
The socket names are pre-shared secrets but all sockets are public right now so anyone who knows or can guess the socket name can join the conversation. We think that this does lack privacy and security. The developers say this is the intended behavior and was designed in a way that nobody can hijack someone’s connection in a socket and no identity is either shared or gathered by the server.
The idea for socket.im was born when a team of 5 developers, who were working in the same environment, needed to share small things like links, pictures and videos to each other. They found that emailing, tweeting or sending things via Facebook takes too long, and wanted a quick way to share things and a way to keep their inboxes clutter free. That is how they came up with the idea to just’ type an URL and share something.’
In the near future, they plan to have reserved sockets (e.g. socket.im/nextbigwhat… etc). These sockets will have owners, who will be able to make a socket private, mute it or have a password to protect it. There is also a rest API on the way, which will be able to connect to anything like a coffee machine to alert you about stuff. The machines will need minimal necessary equipment to connect to socket.im.
Mobile apps and ‘share via socket.im’ kind of features are also planned. One of the priorities of the developers is to put it behind SSL and make it more secure.
The developers are likely to charge for reserved and commercial sockets in the future.
While the service is very basic at present it was very functional and we found ourselves sharing quick messages through the service regularly. We hope the developers implement the planned features as soon as possible and we can see ourselves using this service a lot more.
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Zach Weiner of SMBC-Comics just added an awesome new event on Forekast. Check it out here and let him know that more awesome events like this need to exist in the world.
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Also, we’ve been adding some great features to our new project Forekast.com since launch, and there are many more to come! For a list of some of the improvements go here. Thanks!
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