Mathematics of Games
Responsible: Dr. Lucia Penso
Assistant: Elena Mohr
For: Master Ma/WiMa/MaBi/Finance/Wiwi/CSE/Wirt.Phy/Inf
Type: MATH, 9LP, 4 Hours Course, 2 Hour Exercises (4+2)
Class: Monday 12:15pm-1:45pm in H12 and Tuesday 12:15pm-1:45pm in H20
Exercise Class: Wednesday 2:15pm-3:45pm H15
Important Information: This open course starts on Tuesday, the 23rd April. There is a class instead of an exercise session on the 24th of April.
Exam: First (open) exam: on Friday the 26th of July, 10:00am-12:00pm in Hörsaal Chirurgie (https://www.uni-ulm.de/einrichtungen/kiz/weiteres/campus-navigation/hoersaalfinder/hoersaele/hoersaal-chirurgie/)
Second (open) exam: on Friday the 11th of October, 10:00am-12:00pm in H11.
Short Description: Game theory is the study of multiperson decision problems. Such problems arise frequently in competitive scenarios where knowledge is distributed, such as in economics. For instance, oligopolies incorporate multiperson problems: each one must consider what the others will do in order to achieve success in a competitive environment. The same happens in auctions, where several people might be interested in the very same item. How to act in the best of ways when competition is present among participants with conflictive interests? Does cooperation help in such a scenario? In which cases?
In this class, we will cover a handful of models in game theory, including models of static and dynamic information, as well as of complete and incomplete information. We will also study a variety of stable optimal solutions, including: nash equilibrium, subgame-perfect equilibrium, bayesian equilibrium, perfect bayesian equilibrium.
Several examples are given, such as in the context of oligopolies, auctions, bargaining, tariff and wage competition, cooperative games, finite and infinite repeated games, zero sum games, signaling games, mechanism design, reputation.