Game theory is a mathematical theory dealing with the modeling and the analysis of conflict and cooperation. This interdisciplinary course aims at providing a background and understanding of the main ideas underlying this theory and shows how it can be used for deeper insights into economical, social, political phenomena.
We distinguish between cooperative and non-cooperative (competitive) game theory. In our lecture, we regard the players in a game from a wider point of view so that, e.g., participants in markets, partners in environmental campaigns and even genes from biology, regulating each other, can become “players”. From this regard, it turns out to be natural that the mathematical modeling with networks and dynamical systems becomes very useful.
Cooperative game theory has been enriched in the last recent years through several models which provide decision-making support in collaborative situations under uncertainty. Such models are generalizations of the classical model regarding the type of coalition values. Thus, the characteristic functions are not real-valued as in the classical case - meaning that payoffs to coalitions of players are known with certainty - but they capture the uncertainty on the outcome of cooperation in its different forms: stochastic uncertainty, fuzzy uncertainty, interval uncertainty, ellipsoidal uncertainty.
Involving of certainty into cooperative games is motivated by the real world where noise in observation and experimental design, incomplete information and further vagueness in preference structures and decision making play an important role. This causes a great mathematical challenge which was first approached and well understood in the case of interval-valued uncertainty.
Game theory in all its branches and facets has been of great importance in the areas of the economy. Leading representatives of game theory are among the ones who introduced and developed Experimental Economics, which is mutually related with Game Theory in terms of establishing, analyzing, simulating, testing and, if needed, reoptimizing and improving models, solutions and predictions.
During and at the end of the course we present topics for future research and application.
With this series of lectures that are provided by experienced and enthusiastic researchers, we wish the represent and enjoy the beauty of a central part of modern OR, applied mathematics and economics, and to get further prepared for own scientific research, for building up our countries and serving our people.
Language: English
Duration: 30 academic hours
Tutors of the course:
Prof. G. W. Weber, Institute of Applied Mathematics, Middle East Technical University, Turkey
Dr. Zeynep Alparslan-Gok, Institute of Applied Mathematics, Middle East Technical University, Turkey
Prof. A. Vasin, Operations Research Department, Lomonosov Moscow State University, Russia
Dr. E. Kropat, Institute for Theoretical Computer Science, Mathematics, and Operations Research, University of the Bundeswehr Munich, Germany