KTH Matematik  

Matematisk Statistik


Lecturer and examiner: Jörgen Weibull

Time: 15.15-17.00 the following days:
27 January,
3, 8, 10, 17, 22, 24 February,
3, 22 March,
6 April 13-15 room 3721 (note the change in date, time and place), 12, 28 April.

Final meeting proposed to be May 24th 1315-1700 in 3721.

Place: All the lectures will be held in Room 3733, Department of Mathematics, KTH, Lindstedtsväg 25, floor 7.

Examination: Assignments (inlämningsuppgifter).

Handouts and lecture notes

Course description:

Game theory is a mathematically formalized theory of strategic interactions. In most instances, no single party, decision-maker or player, can determine the outcome single-handedly; the outcome usually depends on several or all participants' actions. Players act on the information at hand, as well as on expectations of others' contemporaneous and future actions. Others' actions depend, in their turn, on their information and expectations about your actions, so all players' actions, information and expectations are intertwined in a complex and fascinating pattern. The analysis of strategic interactions, with due regard to these interdependences, is precisely what game theory is all about. The aim of this course is to present some of the key concepts and results of current game theory in a concise, rigorous and unified way.

The foundations of game theory were laid out in the classic book by John von Neumann and Oscar Morgenstern, The Theory of Games and Economic Behavior (1944). Precursors to this seminal work was a sequence of short papers by Emile Borel in the 1920s and von Neumann's (1928) paper on finite zero-sum games. The most central solution concept in non-cooperative game theory is that of Nash equilibrium, Nash (1950). Harsanyi (1967-68) showed that this solution concept can be generalized to games of incomplete information, in which players do not know each others' goal functions or strategy sets, but form subjective probabilistic beliefs. Selten (1965, 1975) demonstrated how the Nash equilibrium concept could be fruitfully refined for dynamic games and for games in which players make mistakes with (infinitesimally) small probabilities. Alongside these developments, theoretical biologists, notably the late John Maynard Smith, generalized Charles Darwin's theory of natural selection to environments with strategic interactions. This strand of game theory is called evolutionary game theory.

A preliminary plan for the course is as follows: We begin by way of an informal discussion of a few simple examples and proceed to set up some background mathematical machinery. We then define and prove the existence of Nash equilibrium for a general class of games, and discuss two complementary interpretations of this solution concept. Next, we specify the extensive- and normal-form representations, analyze several solution concepts for these, and relate the approaches to each other. We proceed to consider set-valued solutions, and then turn to evolutionary game theory, where we analyze the concept of evolutionary stability and study the replicator dynamic in finite games. Thereafter, we consider two models of recurrent play of games in large but finite populations, each model taking the form of a Markov chain. We analyze two limits of these processes; when the population size tends to infinity and when rationality perturbations tend to zero. If time permits, we conclude by examining so-called Folk-theorems for repeated games.

Literature: The lectures will be based on
1. "Lectures in game theory" (to be distributed during the course)
2. Weibull J: Evolutionary Game Theory, MIT Press 1995.
3. Journal articles.

Till matematisk statistik

Sidansvarig: Filip Lindskog
Uppdaterad: 25/02-2009