Mathematics of the uncertain

Two topics will be covered in the training:

Dr. habil. Hendrik Baumann, Clausthal University of Technology, IASOR:
When intuition plays tricks on us - amazing stochastic statements in a credibility check

Stochastics is probably the mathematical sub-discipline that provides solutions to elementary problems that seem counter-intuitive to many interested parties. These include games of chance, the description of which suggests equal probabilities of winning for the players involved, but in reality these are significantly different. We also encounter such results in other everyday situations, such as waiting for the next bus.

In the lecture, various such problems are addressed and, in addition to the mathematical derivation of the exact results, it is shown how initial assumptions can be checked or refuted using stochastic simulation. It turns out that the steps necessary for implementation in a simulation often already reveal mental errors and can help with the mental acceptance of the results.

Prof. Dr. Stephan Westphal, TU Clausthal, IASOR:
Rock-paper-scissors - Of small and large games, optimal strategies, dilemmas and paradoxes

In game theory, negotiation and conflict situations between individual participants are mathematically modeled and investigated. It is assumed that these players rationally make the decisions that make the most sense for them. In this lecture, we will get to know the basic concepts of non-cooperative game theory, determine optimal strategies for the individual players in selected games and show how these can be calculated with computer support.

Interestingly, these optimal strategies of the individual players often do not lead to an optimal overall result, but may even be far from it for each individual player. We will illustrate this with examples from road traffic, where choosing the route with the least amount of congestion can lead to each road user ending up in a longer traffic jam. We will look at situations where, in contrast, the closure of a road leads to a speeding up of each individual. Finally, we will deal with the question of "mechanism design", i.e. the question of how to design the rules of a game so that the individual players make decisions that come as close as possible to an overall optimum.

Program