Game theory
What do a prime minister, a general, an athlete, a lawyer, a businessman, a psychologist, a spouse and a biologist have in common? Game Theory deals with the study of the behavior of rational beings (those who decide and act on the basis of their logic and “interest”), in situations where they compete or cooperate with others.  Therefore, all of us are faced daily with difficult problems that are at the core of Game Theory, which in conjunction with Mathematics, is indispensable in the understanding of social sciences, including economics, sociology, environmental studies, and psychology.

Probability
Uncertainty is prevalent in our lives. Everyday questions, such as what’s the weather going to be this weekend and whether it’s worth playing a game of chance, or larger-scale questions like how the global climate changes, and how an epidemic develops, or even more exotic ones, such as what is the possibility of life on other planets or the risk of the earth being hit by a celestial body, cannot be answered with complete certainty. Through mathematics and probability theory we can study uncertainty and analyze these situations. 

In this course, we deal with the fundamental concepts of theory and harness its power to study games between people, companies, states and other entities when faced with situations of uncertainty. Students play games, study and analyze them and are led to the most innovative scientific ideas, to make strategic decisions, thereby increasing their profit and/or reducing their damage!

Learning Objectives

• Review and apply the fundamentals of probability to solve mathematical problems, develop an understanding of the theoretical foundations for fundamental models in game theory and model certain types of human behavior in competitive decision-making situations.
• Examine and find the balance (solution) in zero-sum, non-zero sum, signaling, cooperative games, simultaneous and sequential games and utilize real-life and computer simulations to test theories and justify conclusions.
• Share ideas and solutions to problems, both written and orally through individual exercises and collaborative projects or tournaments.

Chance plays an important part in all aspects of life.

We take chances every day: will a shot at goal land in the goal or miss? Will we be caught in a sudden shower or not? How long do we need to wait to be served in our favourite burger house?

Chance or random variation is also a central feature of all working systems: a scientist taking measurements in a lab; a disease spreading through a population; an economist studying price fluctuation. In all these processes some element of chance or randomness are present.  Is it possible to understand and therefore model and analyse such phenomena? If so, what are the tools we need to achieve that? Do we live in a world of randomness, or, as Einstein famously claimed, no one plays dice with the universe?

During this course, we will attempt to “tame randomness” using mathematics as our compass. 

Learning objectives:

• Develop a robust theoretical understanding of the basics of probability theory. 
• Develop the capability to identify the underlying randomness in real life problems, and decide how to model and quantify it.
• Gain an in-depth understanding of the basic technical tools needed in applied probability.
• Make use of random variables and theoretical probability distributions to model simple random processes (Η).