Ateneo - UPO

The course will introduce the basic topics and tools of strategic reasoning and noncooperative Game Theory, aimed to understand some fundamental applications to the theory of the firm.

1) Robert Gibbons, Teoria dei Giochi, Il Mulino 2) C. D. Aliprantis e S. K. Chakrabarti, Games and Decision Making, Oxford university press, 2010. 3) A. Mas- Colell, M.D. Whinston, J. Green, Microeconomic Theory (Chapters on Game Theory)

The course carries 4 ECTS, corresponding to 30 hours of classroom teaching. Of these, approximately 20 hours will be lecture-based teaching (DE) and 10 hours interactive teaching (DI) (including lessons in flipped classroom mode), with the proportions not fixed within each lesson. The aim of the course is to provide students with the basic elements of non-cooperative game theory useful for addressing models of interaction among consumers and among firms. By the end of the course, students will have mastered the analytical tools needed to understand, model, and predict the strategic behavior of economic agents, and will be able to appropriately solve problems in economic and financial contexts involving strategic interaction, using appropriate game-theoretic concepts.

Real valued functions of one and several real variables, optimization, basic notions of probability theory.

Lectures aimed at presenting the topics on the syllabus and discussing them, with an alternation of lecture-based (DE) and interactive (DI) teaching in order to promote student engagement and active participation, including, where possible, through the use of the flipped classroom approach.

Students with disabilities, Specific Learning Disorders (DSA) or Special Educational Needs (BES) can request dedicated services and tools from the University's Staff for Career Development and Student Services, consulting the dedicated University webpage. After contacting the University Staff, they can contact the instructor in charge of the module regarding the specific examination arrangements.

Assessment of learning for this module consists of a compulsory written test and an optional oral exam.

The test consists of one theoretical question (max 8 points) and two applied exercises (max 9 points each), designed to assess knowledge of the constituent elements of a game and the properties of equilibria, and the ability to solve games in normal and extensive form. To pass, students must know the fundamental elements of game theory, be able to solve standard problems, and correctly use the discipline's terminology.

Criteria: Sufficient (18–20): knowledge of fundamental concepts and essential understanding of the properties of equilibria; fully solves at least one of the two exercises and sets up the other, with sufficient knowledge of the theoretical question. Good (21–24): good knowledge and understanding, fair application ability; correctly solves both exercises, applying best reply and/or mixed strategies where required, with a fair level of theoretical understanding. Excellent (25–26): thorough knowledge, full application ability including variants; answers correct, complete, rigorous, with complete theoretical justifications.

Oral exam (optional): may only be taken with a passing mark in the written test; consists of the discussion of a short scientific paper or a topic not covered in class, chosen by the student from a list published on the course webpage. It assesses independent learning ability, communication skills, and the ability to connect the various topics. It must be taken in the same exam session as the written test and can raise the mark by up to a maximum of 7 points, up to an overall maximum of 30 cum laude.

The final mark for the integrated course is agreed collegially by the instructors responsible for the two modules, based on the written test results and on what is observed in any oral exams, also considering the student's ability to connect the two disciplinary areas; it is not necessarily the arithmetic mean of the two marks.
Due to the integrated nature of the course, the exams for both modules must be taken and passed in the same session, otherwise the mark loses validity.

Registration for the written test via the student portal is mandatory: once the maximum number of exam attempts allowed under the Teaching Regulations has been reached, the system will not permit further registrations.

Elements of non-cooperative game theory; games in normal and extensive form; Nash equilibrium, mixed strategies; backward induction and subgame perfect equilibrium; an introduction to repeated games and Bayesian games; elements of cooperative game theory with transferable utility: the core, the Shapley value.

The two modules of the integrated course run in parallel throughout the semester, with a teaching schedule synchronized between the instructors, so that the presentation of the various game theory topics always precedes the analysis of the models in the Consumer Theory and Theory of the Firm module in which they are required.

-Knowledge and understanding: recognizing a situation of strategic interaction between decision-makers; identifying the constituent elements of a game in normal or extensive form.
-Applying knowledge and understanding: finding the solutions of a game already represented in strategic or extensive form; translating and representing a real-world situation of strategic interaction in game form; moving from normal form to extensive form and vice versa; finding the equilibria of a game using best reply functions and mixed strategies; adapting the choice of tools to the variants required.
-Making judgements: evaluating which solution concept is most appropriate for a given game (non-cooperative or cooperative), and assessing the plausibility of the rationality and information assumptions underlying a model.
-Communication skills: communicating clearly and rigorously the logical-deductive reasoning followed in addressing problems; connecting the various topics of the integrated course.
-Learning skills: at a sufficient/average level, independently using texts and materials to understand and solve standard problems; at an advanced level, also the ability to independently explore topics not explicitly covered in class, including through the study of short scientific papers.