The goal of this course is giving the student a background in the methodologies in the advanced design of mechanisms using non-lineal convex optimization and game theory. The program will cover from basic concepts related to convexity, convex optimization problems, Game Theory, Nash Equilibria, to applications of these methodologies to networking such as resource allocation, back-pressure models, power-control models compressive sensing, game theory in wireless networks, pricing models in networks, game theory in routing problems or incentives in P2P systems.
Person in charge
Jose Maria Barceló Ordinas (
Technical Competences of each Specialization
Computer networks and distributed systems
CEE2.1 - Capability to understand models, problems and algorithms related to distributed systems, and to design and evaluate algorithms and systems that process the distribution problems and provide distributed services.
CEE2.2 - Capability to understand models, problems and algorithms related to computer networks and to design and evaluate algorithms, protocols and systems that process the complexity of computer communications networks.
CEE2.3 - Capability to understand models, problems and mathematical tools to analyze, design and evaluate computer networks and distributed systems.
CTR6 - Capacity for critical, logical and mathematical reasoning. Capability to solve problems in their area of study. Capacity for abstraction: the capability to create and use models that reflect real situations. Capability to design and implement simple experiments, and analyze and interpret their results. Capacity for analysis, synthesis and evaluation.
Capacity to formulate a convex optimization problem
Capacity to apply convex optimization to networking problems.
Capacity to understand what game theory is and how a game is solved.
Capacity to apply game theory to networking problems
Convex Optimization basics
Convex sets, convex functions, convex optimization problems (COP) and duality (Lagrange dual function, KKT optimality conditions), methods for solving COP's (General Descent Methods, Interior Point Methods)
Convex Optimization Applications to networking
Exxamples on Resource allocation in networks, back-pressure, Power control, Publish-subscribe in DTN, Compressive Sensing.
Game Theory basics
Strategic and Extensive Forms of a Game, Non cooperative Games (Nash pure and mixed equilibria, correlated equilibria), Cooperative Games (core of a game, Shapley values, Nash Arbitration scheme), cost-sharing (Braess Paradox, Price of Anarchy and Stability), Auctions.
Game Theory Applications to Networking
Wireless Networking games, Energy-Efficient Power Control games, pricing, P2P games
During the initial sessions of each topic, the main results will be explained in the blackboard. the student will solve some exercises to prove their skills in the topic. Finally, there will be some sessions devoted to discuss in the classroom models taken from research papers that apply the related topics.
The evaluation is based on different activities
- Short projects and presentations in which the student has to deliver and defend the obtained results (P)
- A final exam (FE)
Each of the activities will be evaluated (0=
The final mark for the course (FM) will be:
Where P=(1/N) x Sum (Pi) with i=1,...N
with Pi the projects and oral presentation mark. There will be a minimum of 2 practical projects and 1 oral presentation.
Geometric Programming for Communication Systems -
Mung Chiang, Foundations and Trends® in Communications and Information Theory ,
Volume 2 Issue 1-2 .
ISBN: 1-933019-09-3 www.princeton.edu/~chiangm/gp.pdf