Many networks today are simultaneously built, operated, and used by multiple parties with a diverse set of goals and with constantly changing degree of cooperation and competition. The future of much of the complex technology developed today depends on our ability to successfully build and manage systems used by such diverse set of users, ensure that participants cooperate despite their diverse goals and interests. Examples include a wide range of networks military, though transportation networks, and Information networks like the Web and the Internet. Such large and decentralized networks provide amazing opportunities, but it also presents large challenges. The future of much of the complex technology developed today depends on our ability to successfully build and manage systems used by such diverse set of users, ensure that participants cooperate despite their diverse goals and interests.One focus of the project was algorithmic game theory, and it aimed to understand what are simple and natural frameworks that lead to efficient systems for such heterogenous user sets. We revisited some traditional algorithmic questions, such as network design, from the perspective of building networks for heterogenous users. The main focus of the research was to approach some of the traditional algorithmic questions in networks from the perspective of game theory. We mostly focused on the quality of stable solutions obtained by selfish users, but also started to consider cooperative behavior of users.A related focus was approximation algorithms. We considered approximation algorithms for some of the related optimization problems. We developed approximation algorithms for problems of influence maximization, graph partitioning problems, facility location with heterogenous user sets, and disjoint path problems.In addition to the new research reported below, I also spend time during the last three years writing a textbook on Algorithm Design (with Jon Kleinberg) that had now been adopted by a number of school as their textbook for the undergraduate or graduate algorithms course. This past year PI tva Tardos have been editing a collected volume on Algorithmic Game Theory (with Nisan, Roughgarden, and Vazirani) that appeared this fall. I have co-authored three of the 29 chapters of the book. I wrote an introduction to game theory for computer scientist (with Vijay Vazirani), an introduction to "Price of anarchy" (with Tim Roughgarden), the area working to evaluate the quality of equilibria in games. Finally, I also wrote a survey on the current state of the art on network formation games (with Tom Wexler), and area that will be important both for understanding physical networks like the Internet, and also for understanding emerging social 1 20080107187 networks the face-book. These networks are stile in the developing stages, and our understanding can hopefully lead to design that will significantly enhance all of our lives. In a wide range of markets, individual buyers and sellers often trade through intermediaries, who de...