3

2018-2019

01001423

Mathematics

Portuguese

Face-to-face

SEMESTRIAL

6.0

Elective

1st Cycle Studies

Basic courses in probabilities and statistics, analysis, linear algebra and linear programming.

Classes of two types: classes where the professor presents the theoretical concepts and examples, and classes for exercises discussion and problem solving. Extensive tutorial time is offered to the students to support the solution of the homework assignments and preparation for the various exams.

Expose students to the mathematical modeling of strategic behavior. Various types of games (zero-sum and general sum, cooperative and noncooperative, static and dynamic, with or without transfer of utilities) are analyzed. In some cases, the goal is to predict the behavior of players in future situations, in other cases, it is possible to find satisfactory solutions to all players. The interdisciplinary nature of this course makes it appealing to students of management, computer science, economics, mathematics, political science, statistics, etc.

This course aims at developing the following skills: knowledge of mathematical results, ability to formulate and solve problems; conception or application of mathematical models to real situations. On the personal level it also allows to develop written and oral expressions, competence in the use of computational tools, individual initiative and teamwork, the ability to do research and independent learning and critical thinking.

• Zero-sum games (Strategic form, matrix games, domination, the principle of indifference, solving finite games, the extensive form of a game, recursive and stochastic games, models with continuous strategies)

• General-sum games (cooperative and noncooperative games, Nash equilibrium, models of duopoly, cooperative games with and without utility transference, Nash bargaining solution)

• Games in coalitional form (imputations, the core, the Shapley value, the nucleolus)

• Impartial combinatorial games (Take-away games, nim, sums of combinatorial games, graph games)

João Eduardo da Silveira Gouveia

Final assessment

*Oral presentation: 10.0%*

*Exam: 90.0%*

Continuous assessment

*A set of homework assignments handed in individually: 5.0%*

*Oral presentation: 10.0%*

*Frequency: 85.0%*

T, Ferguson, Game Theory, Department of Mathematics, UCLA, 2005 (disponível na página-web do autor).

R. Gillman, D. Housman, Models of Conflict and Cooperation, American Mathematical Society, 2009.

M. Mesterton-Gibbons, An Introduction to Game-Theoretic Modelling, American Mathematical Society, 2000.

R. Gibbons, A Primer in Game Theory, Prentice-Hall, 1992.

P. Klemperer, Auctions: Theory and Practice, Princeton University Press, 2004.