Oslo Summer School in Comparative Social Science Studies 2001


Evolution, Rationality and Equilibrium in Games

Lecturer: Professor Jörgen W. Weibull,
Stockholm School of Economics, Sweden
Dates: 6. - 10. August 2001


Objectives
The traditional interpretation of game theory is that the game in question is played exactly once by perfectly rational players who know the game, whose knowledge of the game and of each others' rationality is common or mutual knowledge, and who hold interpersonally consistent expectations of each others' play. Recently, evolutionary interpretations have been developed where the game is instead recurrently played by boundedly rational individuals who are randomly drawn from large populations. These individuals need not know much about the game, but adjust their strategy choice in the light of individual or social experience from play. Equilibrium may then arise in the long run, as dynamically or stochastically stable states at the population level. However, in many games the evolutionary predictions are not equilibrium points but sets containing equilibria. The course aims at explaining some of the key concepts and results in the evolutionary paradigm and to relate those to concepts in the rationalistic.


Basic readings


Outline of lectures

Lecture 1: Introduction
A brief history of game theory. Game theory as a research tool. Rationalistic and evolutionary interpretations. Extensive, normal and characteristic forms. Examples. The course outline. [Binmore (1986,1987), vanDamme (1987), vanDamme-Weibull (1995), Kandori (1996)]


Lecture 2: Rationality
Normal form games. Dominance relations. Iterated elimination of dominated strategies. Best replies and rationality. Rationalizability. Sets closed under rational behavior. Examples. [Pearce (1984), Basu-Weibull (1991), Aumann-Brandenburger (1995), Weibull (1995)]


Lecture 3 Equilibrium
Best replies and Nash equilibrium. The structure of the set of Nash equilibria. Perfection. Strategic stability. Essentiality. Sets closed under rational behavior. Examples. [Selten (1975), Kohlberg-Mertens (1986), vanDamme (1987), Weibull (1995), Ritzberger-Weibull (1995)]


Lecture 4: Evolutionary stability
Symmetric two-player games. Definition of ESS. Characterizations of ESS. Relation to perfection. Social efficiency in doubly symmetric games. Examples. [vanDamme (1987), Weibull(1995)]


Lecture 5: Boundedly rational strategy choice
Micro models of boundedly rational social learning. Satisficing and imitation. Comparison and imitation. Experimentation. Noisy and smooth myopic best replies. Induced stochastic population processes. [Binmore-Samuelson-Vaughn (1995), Benaïm-Weibull (2000)]


Lecture 6: Tools for deterministic dynamic analysis
Vector fields. Solution mappings. Trajectories and orbits. Invariance and stationarity. Stability concepts. Attractors.[Weibull (1995)]


Lecture 7: Deterministic dynamic approximation of stochastic evolution
The mean-field equation. Approximation over bounded time intervals. Bounds on exit times. Empirical visitation rates. Large deviations. The radius and co-radius of attractors. [Binmore-Samuelson-Vaughn (1995), Ellison (2000), Benaïm-Weibull (2000)]


Lecture 8: Evolution, rationality and equilibrium
The two versions of the replicator dynamics. Examples. General classes of selection dynamics. ''As if'' rationality, and ''as if'' knowledge of rationality, in the long run. Nash equilibrium. Sets closed under better replies. Coordination games. .[Weibull (1995), Ritzberger-Weibull (1995), Hofbauer-Weibull (1996), Benaïm-Weibull (2000)]


Lecture 9: Perpetually perturbed best reply dynamics
The evolution of social conventions. Stochastic stability. [Kandori-Mailath-Rob (1993), Young (1993, 1998), Bergin-Lipman (1996), vanDamme-Weibull (2001)]


Lecture 10: Concluding discussion
Contrasting rationalistic and evolutionary predictions. Robust set-valued predictors. Extensive-form analysis. Laboratory experiments. Testing.


Readings


The lecturer
Jörgen W. Weibull is A.O. Wallenberg professor of economics at the Stockholm School of Economics. His main area of reseach is game theory, both concerning its foundations and its applications to economics, in particular to political economy modelling.