Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 5.
Revision Protocols and Evolutionary Dynamics
1 / 28
Population Games played by Boundedly Rational
Agents
We have introduced the idea of a population game, a game
played by a large popu
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 9.
Local Stability
1 / 26
Local Stability
Where global convergence does not occur (or cannot be
proved), we can at least say something about the local
stability of the rest points of an e
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 10.
Nonconvergence of Evolutionary Dynamics
1 / 21
Outline
In this lecture, we shall further explore the conditions under
which an evolutionary dynamic is locally stable.
Once again we s
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 11.
Stochastic Evolution and Stationary Distributions
1 / 38
Outline
So far, we have focussed exclusively on the behavior of the
mean dynamic, which we have treated as a (deterministic)
a
University of California, Irvine
Econ 243B Advanced Game Theory
Evolution & Learning in Games
Sample Final Exam
Instructor : Jean-Paul Carvalho
Due: xxxx June 2013
Please print legibly (or type your answers)
Name:
Student ID number:
Please answer all ques
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 12.
Stochastic Stability
1 / 38
Analyzing Large-Dimensional Markov Processes
We have seen that stationary distributions for reversible
Markov processes can be computed.
We are still left
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 8.
Global Convergence of Evolutionary Dynamics II
1 / 16
Supermodular Games
Supermodular games are games that exhibit strategic
complementarities.
The strategy set S = cfw_1, 2, ., n is
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 7.
Global Convergence of Evolutionary Dynamics I
1 / 20
Global Convergence
Last week, we examined the connection between the rest
points of various dynamics and Nash equilibria of the
und
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 2:
Foundations of
Evolution & Learning in Games II
Outline
In this lecture, we shall:
Take a rst look at local stability. In particular, we shall dene
an evolutionary stable state and exp
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 1:
Foundations of
Evolution & Learning in Games I
Classical Game Theory
We repeat most emphatically that our theory is
thoroughly static. A dynamic theory would
unquestionably be more comp
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 3.
Population Games I:
Introduction and Potential Games
1 / 38
Population Games
1. Number of agents is large,
2. Individual agents are small,
3. Anonymous interaction,
4. The number of rol
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 4.
Population Games II:
Stable Games and Supermodular Games
1 / 35
Population Games
Let us consider two more classes of population games, for which
there exists a substantial body of resul
Evolution & Learning in Games
Econ 243B
Jean-Paul Carvalho
Lecture 6.
Properties of Deterministic Dynamics
1 / 48
Properties of Deterministic Dynamics
Let us now examine specic properties of dierent revision
protocols and mean dynamics.
The properties s
Econ 243B Advanced Game Theory
Evolution & Learning in Games
Solutions: Sample Final Exam
Q1. (a) Dene:
U 1 = (U 2 ) =
Then:
F (x1 , x2 ) =
0
U2
2 4
00
.
U1
0
x1
x2
.
(b) We know that x is a regular Taylor ESS if and only if x is a quasistrict Nash equili