GAMES AND STRATEGIES

GAMES AND STRATEGIES

Roberto Lucchetti, Xavier Mathieu Raymond Venel

Instructional goals

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.

Intended learning outcomes

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.

Course Contents

Fundamentals of non-cooperative and cooperative game theory.

Reference Books

Textbooks -Anna R. Karlin and Yuval Peres (2016). Game Theory Alive, American Mathematical Society. -Slides 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).

Teaching Methods

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

Assessment Method

The exam consists in a written part with several exercises where the student, by solving some exercises, must demonstrate understanding of the main topics of the course. The student will be able to suitably model economic and managerial situations in terms of games and to find the corresponding solutions. For the purposes of assigning a mark out of thirty, the following evaluation criteria will be taken into account: Ability to model real-life problems with games; Capability to find the suitable solutions of the proposed games. There will be a possibility to obtain bonus points during the semester. During the whole course, 4 tests will be proposed, to solve in presence on personal device. Each test will be graded over 10 and the date of the tests will not be announced in advance. At the end of the semester, the teacher will compute the sum of the best three tests. The students will have the following bonuses depending on the result - sum from 20 (included) to 23 (included): 1 point - sum from 23 (excluded) to 27 (included): 2 points - sum from 27 (excluded) to 30 (included): 3 points The bonus points are only valid for an exam grade obtained at the first or the second session. They will not be taken into account for other sessions. The final mark for the course is determined by the sum of the grades obtained in the various exercises in the exam, whose maximum grade is known to the students, plus the bonus, if obtained, according to the previous rules. The teacher reserves the right to have an oral examination if the written exam leaves some doubts.

Thesis assignment criteria

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

Week 1 Contenuto sessioni on line e on campus

Introduction to the Course -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...

Week 2 Contenuto sessioni on line e on campus

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)

Week 3 Contenuto sessioni on line e on campus

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

Week 4 Contenuto sessioni on line e on campus

Zero sum games -Examples -Conservative values -Nash equilibria as pairs of solutions of two linear problems in duality.

Week 5 Contenuto sessioni on line e on campus

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

Week 6 Contenuto sessioni on line e on campus

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

Week 7 Contenuto sessioni on line e on campus

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

Week 8 Contenuto sessioni on line e on campus

The Shapley value -Simple games and other semivalues

Week 9 Contenuto sessioni on line e on campus

Mechanism Design -The VCG mechanism

Week 10 Contenuto sessioni on line e on campus

Social choice -The May theorem -The Arrow theorem -The Gibbard Satterwhite theorem -Restricted domains

Week 11 Contenuto sessioni on line e on campus

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

Week 12 Contenuto sessioni on line e on campus

Matching problems -Algorithms for matching -Partial order on matchings