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I am doing a senior project and it must be based off game theory, but I am having trouble finding any connections to engineering, possibly structural, or architectural, maybe even civil or mechanical. Are there any branches of engineering that use a significant amount of game theory?

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You might want to consider Noam Nisan's book - cambridge.org/journals/nisan/downloads/Nisan_Non-printable.pdf , and maybe try to look in Noam's blog, he has some nice stuff in there which should be related to your interests. –  Asaf Nov 6 '11 at 8:55

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A Spring 2010 course was offered by Asu Ozdaglar @MIT, entitled "Game Theory with Engineering Applications." It is incluede in MIT's Open CourseWare, so extensive information is available. Here is the course description:

Course Description. This course is an introduction to the fundamentals of game theory and mechanism design. Motivations are drawn from engineered/networked systems (including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, multi-agent systems, pricing and investment decisions in the Internet), and social models (including social and economic networks). The course emphasizes theoretical foundations, mathematical tools, modeling, and equilibrium notions in different environments.
          
(The point of this image is that the stag hunt is "a game which describes a conflict between safety and social cooperation.")

Here is a high-level syllabus of this course:

  1. Introduction to game theory
  2. Strategic form games
  3. Learning, evolution, and computation
  4. Extensive games with perfect information
  5. Repeated games
  6. Games with incomplete information
  7. Mechanism design
  8. Mechanisms in networking

See also the LLNL (U.S. Lawrence Livermore National Laboratory) Optimization and Game Theory project, which they describe as follows:

Researchers apply a wide range of optimization and game theory techniques to address challenging problems in national security, energy economics, and environmental management. Our problems typically involve complex objectives in multiple dimensions (e.g., improving safety while reducing cost), and uncertainty of the outcomes of actions. Problems can require high-resolution models or national-scale infrastructure, so efficient algorithms are required that exploit problem structure and large-scale computational hardware.

Finally, I will mention the 2006 (short) book, Game Theory for Wireless Engineers, whose abstract contains these two sentences:

In the early to mid-1990's, game theory was applied to networking problems including flow control, congestion control, routing and pricing of Internet services. More recently, there has been growing interest in adopting game-theoretic methods to model today's leading communications and networking issues, including power control and resource sharing in wireless and peer-to-peer networks.

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