There is no standard definition of "Information economics". If you are interested in the economics of the IT industry then apart from Varian's "Information Rules" mentioned in another comment, there is

* Oz Shy, The Economics of Network Industries.

If you are interested in research at the interface of economics and theoretical computer science you have:

* Shoham, Leyton-Brown. Multiagent Systems.

* Nisan, Roughgarden, Tardos, Vazirani. Algorithmic Game Theory.

* Cramton, Shoham, Steinberg, Smith. Combinatorial Auctions.

For the traditional economic theory of asymmetric information among economic agents:

* Bikchandani, Riley and Hirshleifer. The Analytics of Uncertainty and Information.

Studied economics in college. The two books we read on information economics were Rethinking the Network Economy by S J Liebowitz and Information Rules by Varian and Shapiro.

I found Information Rules to be the superior text. They are both around 10 years old however, something more current may be more desirable.

The Wealth of Networks by Yochai Benkler and Information Rules by Hal Varian are good. Both are a bit dated though. If you know of any contemporary works to those, I'm all ears.