Educational offer - University of Padova

Syllabus

Prerequisites:	A course, even a basic one, on probability theory.
Target skills and knowledge:	The course involves the acquisition of the following elements of knowledge and proficiencies, divided in two sets. (1: basic objectives) To learn and master basic and advanced theoretical concepts of game theory and to know how to solve general multi-objective multi-agent problems with game theory techniques. (2: applied objectives) To be able to apply game theory concepts to practical scenarios, especially in the ICT context; in particular, it is relevant to contextualize game theory as an instrument for the evaluation of the effectiveness of the solution process in distributed multi-agent procedures. According to the enrollment/frequency/mutuation of the student, the importance of these two sets is considered differently. In particular, applied objectives are achievable only by engineering students that are regularly attending the course. For students belonging to different programs and/or not regularly attending lectures, the acquisition of knowledge and skills focuses on the first set of basic objectives.
Examination methods:	For the students of engineering programs with regular attendance to the course (differently from other kinds of students), the exam involves the development of a project in 1-3 person groups, on course-related topics applied to ICT. This is agreed half-way through the course together with the lecturer. For all the students, in any event the exam also includes a mandatory open-book written test, containing four problems of game theory focusing on different topics of the course. Every exercise involves three questions. For engineering students with regular attendance to the course, the written test is limited to solving three exercises out of four. For the other students (non-engineering students or students without regular attendance), the written test involves all of the four exercises. If the written test is sufficient, non-engineering students or students without regular attendance can directly finalize the passing score. Engineering students with regular attendance instead discuss their project with an oral exam after the written test. Oral exams are scheduled in the same day of written tests (even though students can decide to give the two parts on separate days). Both the written test and the oral exam must be sufficient to pass.
Assessment criteria:	Every question in the written exam awards up to 3 points. For engineering students with regular attendance, the project discussion awards up to 10 points. The final mark is the numerical sum of the scores achieved in the questions and the project discussion (if present), capped to 30. Honors are awarded to students with a final numerical score higher than 31. Every question in the written test will be evaluated according to: - pertinence, correctness, and completeness of the answer; - proper usage of terminology, methodology, and formal representations of game theory; - acquired attitude towards problem solving - attitude towards discussion and ex-post verification of the solution found For the project evaluation (if present), the following aspects will be considered: - originality of the proposal, and their pertinence with both the course topics and the engineering methodologies in ICT contexts - quality of the oral exposition - attitude towards teamwork and the presence of individual contributions relatable to every single participants - attitude towards drawing meaningful conclusions from a scientific standpoint thanks to the methodologies learned during the course
Course unit contents:	Basic concepts of game theory Utility, market, discount factor Static games in normal form Dominance, Nash equilibrium Efficiency, price of anarchy Zero-sum games, minmax games Mixed strategies, mixed equilibria Nash theorem, minmax theorem The tragedy of the commons Dynamic games Strategy and subgames Backward utility Stackelberg equilibria Repeated games and cooperation Dynamic duopolies, collusion Cooperation, pricing Imperfect/incomplete information Bayesian games, signaling, beliefs Revelation principle Axiomatic game theory Fictitious play Best response dynamics Distributed optimization Algorithmic game theory Computation, complexity, and completeness of equilibria Auctions, bargaining First-price and second-price auctions VCG principle Cooperative games: the core, the Shapley value Resource allocation Utilities, choices, and paradoxes Potential games, coordination Bio-inspired algorithms Evolutionary games Cognitive networks Selfish routing Game-theory enabled multiple-input systems
Planned learning activities and teaching methods:	Conventional lectures with slides/projector support. Interaction via the moodle platform.
Additional notes about suggested reading:	Several books treat game theory from a general point of view. Just as a suggestion, you can use Tadelis' book as a reference from a general perspective. This ought to be integrated with other material about applications. MacKenzie and DaSilva's book is a good example, even though it is not mandatory to use a book to this end (material found to the internet could also work). In any event, the lecturer will provide the students with additional booklets and all the lecture notes.
Textbooks (and optional supplementary readings)	S. Tadelis., Game Theory: An Introduction.. --: Princeton., 2013. A. MacKenzie, L. DaSilva, Game Theory for Wireless Engineers. --: Morgan&Claypool, 2006. Noam Nisan, Tim Roughgarden, Eva Tardos, Vijay V. Vazirani (eds.), Algorithmic Game Theory. --: Cambridge Univ. Press, 2007. Roberto Lucchetti, A Primer in Game Theory. --: Esculapio, 2011.