GAMES AND STRATEGIES

GAMES AND STRATEGIES

Roberto Lucchetti, Xavier Mathieu Raymond Venel

Obiettivi formativi

The course will make the students familiar with interactive decision theory. Students will be able to analyze and solve simple problems in the fields of economics, management, and finance, using the techniques of game theory.

Risultati di apprendimento attesi

Knowledge and understanding: The aim of the course is to provide students with the basic tools of interactive decision theory in order to be able to analyze and solve simple theoretical and applied problems in economics, management, and finance, by means of game theoretic techniques. Applying knowledge and understanding: Students will be able to analyze simple problems in interactive decision, with special attention to economic problems, managerial issues, international relations, and bargaining contexts. Criticism of judgment: At the end of the course, students will know the specific tools of the strategic analysis in order to understand economic phenomena. Students will be stimulated to solve standard and less standard exercises and problems in order to develop a critical ability in analyzing economic, managerial, and financial problems. Communication skills: Students will be stimulated to develop communication skills by presenting solutions to exercises and participating in discussion during classes. Learning skills: Students will pursue adequate skills and knowledge to improve their skills in modeling and solving simple economic, managerial, and financial problems. This will have an important positive impact at the moment of analyzing more complex situations.

Contenuti Del Corso

Fundamentals of non-cooperative and cooperative game theory.

Testi Di Riferimento

Textbooks -Anna R. Karlin and Yuval Peres (2016). Game Theory Alive, American Mathematical Society. -Slides and notes provided by the teachers. -Exercises provided by the teachers and tutors Other useful readings - Michael Maschler, Eilon Solan, and Shmuel Zamir, Game Theory, Cambridge University Press (2013). - Martin J. Osborne, An Introduction to Game Theory, Oxford University Press (2003). - Levent Kockesen and Efe A. Ok, An Introduction to Game Theory (2007). - Joel Watson, Strategy: An Introduction to Game Theory, 3rd Edition, W. W. Norton & Company (2013). - Ein-Ya Gura and Michael Maschler, Insights into Game Theory, Cambridge University Press (2008). - Noam Nisan, Tim Roughgarden, Eva Tardos, Vijay V. Vazirani, Algorithmic Game Theory, Cambridge University Press (2007).

Metodologie Didattiche

Interactive learning. During classes students will be asked to offer solutions to problems proposed by the teacher.

Modalità di verifica dell'apprendimento

The final grade for this course evaluates the student’s ability to model economic and managerial scenarios using game theory and to identify the corresponding equilibrium solutions. The assessment consists of two main components: the Midterm and the Final Exam. The Midterm Assessment A midterm exam will be held halfway through the semester and will cover the first part of the course. It is graded out of 17 points and accounts for half of the final grade. After the results are published, students have seven calendar days to formally accept or reject their mark via the My Luiss platform. Only grades of 9/17 or higher can be accepted. If you do not accept or reject the grade within this period, it will be automatically accepted. Students who miss the midterm, score below 9, or choose to reject their grade must take the full version of the Final Exam (both the Recovery and General sections). Accepted midterm grades remain valid for all exam sessions within the same academic year, even if a student withdraws from a final exam session. If the course is not completed within the academic year, the midterm grade expires. The Final Examination The final exam consists of two sections: General Section (mandatory for all students): covers the second half of the course Recovery Section (only for students without an accepted midterm): covers the first half of the course For students with an accepted midterm, the final grade (out of 30) is the sum of: Midterm (out of 17) General Section (out of 17) If a student has an accepted midterm, any answers provided for the Recovery Section will not be considered. For all other students, the final grade is based on the Recovery and General sections taken in the same exam session. The final exam is a single, indivisible assessment: the two sections cannot be accepted or rejected separately. In accordance with university regulations, the final grade cannot be refused. Exam Rules and Conduct Exams are closed-book: textbooks and personal notes are not allowed. An official reference formula sheet will be provided during the exam. The use of any communication device is strictly prohibited. Any violation will be reported to the Rector for disciplinary action. Attendance Bonus Students who attend more than 75% (resp. 85%) of the scheduled teaching hours (including lectures and exercise sessions) will receive a bonus of 1 point (resp. 2)added to their final grade. This bonus applies only to the first and second exam sessions immediately following the end of the course. It will not apply to later sessions. Attendance is monitored through the Luiss App system and additional random checks during the semester. Any attempt to misrepresent attendance will result in no bonus points and a penalty of −2 point on the final grade. Oral Examination The instructor reserves the right to require an oral examination to confirm the grade if deemed necessary.

Criteri per l’assegnazione dell’elaborato finale

Solid understanding of the material, verified through a conversation with the teacher.

Settimana 1

Matching problems -One-to-one and many-to-one matchings -Stable matchings

Settimana 2

Matching problems -Algorithms for matching -Partial order on matchings

Settimana 3

Cooperative games -Transferable utilities and coalitions -Examples -Solutions of cooperative games -Imputation and core -The core in simple games.

Settimana 4

The Shapley value -Simple games and other semivalues

Settimana 5

Mechanism Design -The VCG mechanism

Settimana 6

Introduction to non-cooperative games -Games in strategic form -Solution concepts: elimination of dominated strategies, Nash equilibrium - Examples finite games: prisoner's dilemma, tragedy of the commons, battle of the sexes, doves and hawks...

Settimana 7

Mixed strategies and Continuous game - Mixed extension of a finite game - The Nash theorem of existence of equilibria for strategic games -Examples: Finite game and Continuous Game (Cournot Competition, Hotelling)

Settimana 8

Extensive form games -Game trees -Solution by backward induction -Subgame perfection - Examples: Stackelberg competition

Settimana 9

Zero sum games -Examples -Conservative values - Maxmin/minmax strategies - Examples : Nim games

Settimana 10

Potential games -The notion of potential and how to find it -Local maxima and equilibria in pure strategies -Convergence of Best Response Dynamics -Price of Anarchy and Price of Stability

Settimana 11

Evolutionary and Correlated equilibria - Evolutionary Stable Strategy - Correlated equilibrium and Mediator - Examples

Settimana 12

Repeated games : Folk Theorem