Obituary: John Maynard Smith

Robert Karl Stonjek said:

John Maynard Smith dies Evolutionary biologist applied
game theory to evolution, defended neo-Darwinism By
Catherine Brahic

One of the most renowned and influential evolutionary
biologists of his generation, John Maynard Smith, died of
lung cancer on April 19, at the age of 84.

Maynard Smith was probably most widely known for applying
game theory to evolutionary biology. Originally developed
in 1944 by John von Neumann and Oskar Morgentern, game
theory is a mathematical model used by economists to study
the outcomes of interactions between "collaborators" and
"enemies" in situations in which neither can entirely
predict the actions of the other, but can adapt their
behavior according to what they see the other doing.

Maynard Smith applied game theory to interactions between
competing individuals of the same species that use
different stratagems for survival.

Imagine combat in which each individual must decide
whether or not to escalate the fight without knowing his
opponent's decision. Maynard Smith showed, with George
Price, that the interests of both combatants are best
served if both decide not to escalate the fight.

I heard somewhere that Smith actually employed Nash
equilibria formulations. You know, the guy the movie 'A
Beautiful Mind' was based on. If I'm wrong about this, I
would certainly like to know it, because I've repeated it to
a number of people. It makes for a hell of an interesting
story and brings ev science much closer to home for lots of
folks. Comments anyone?

PR

in article [email hidden], Phil Roberts, Jr. at
[email hidden] wrote on 4/26/04 9:47 PM:

Quoted message said:

I heard somewhere that Smith actually employed Nash
equilibria formulations. You know, the guy the movie 'A
Beautiful Mind' was based on. If I'm wrong about this, I
would certainly like to know it, because I've repeated it
to a number of people. It makes for a hell of an
interesting story and brings ev science much closer to
home for lots of folks. Comments anyone?

John Maynard Smith was a major player in the early
development of game theory, and its primary proponent in
applying game theory to biological systems. If you pay close
attention to the dialogue in the movie "A Beautiful Mind"
you will here a quick comment toward the end to the effect
that Nash thought those non-mathematicians applying game
theory in scientific contexts like Biology were messing it
all up. I am pretty sure that he was referring specifically
to Maynard Smith. I am not saying that I agree with Nash,
but AFAIK he did not have much respect for Maynard Smith.

Guy

"Phil Roberts, Jr." <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

I heard somewhere that Smith actually employed Nash
equilibria formulations. You know, the guy the movie 'A
Beautiful Mind' was based on. If I'm wrong about this, I
would certainly like to know it, because I've repeated it
to a number of people. It makes for a hell of an
interesting story and brings ev science much closer to
home for lots of folks. Comments anyone?

According to Myerson's textbook "Game Theory", an ESS is a
Nash equilibrium with some extra conditions. It is stable in
a stronger sense. However, a Nash equilibrium always exists
- an ESS need not.

[email hidden] (Jim Menegay) wrote in message news:<[email hidden]>...

Quoted message said:

"Phil Roberts, Jr." <[email hidden]> wrote in
message news:<[email hidden]>...

Quoted message said:

I heard somewhere that Smith actually employed Nash
equilibria formulations. You know, the guy the movie 'A
Beautiful Mind' was based on. If I'm wrong about this, I
would certainly like to know it, because I've repeated
it to a number of people. It makes for a hell of an
interesting story and brings ev science much closer to
home for lots of folks. Comments anyone?

According to Myerson's textbook "Game Theory", an ESS is a
Nash equilibrium with some extra conditions. It is stable
in a stronger sense. However, a Nash equilibrium always
exists - an ESS need not.

Here is something else I just learned about the relationship
between Nash and ESS. As you may know, the usual economic or
political interpretation of a mixed strategy is that a
rational game player will randomize responses (because being
predictable can be a disadvantage). In biological
applications, however, the two players are randomly chosen
from a population, and the individual doesn't need to
randomize - the population does it for him. When traditional
game theorists first became aware of how biology had
reinterpreted the meaning of mixed strategies, they
considered this a major innovation - nothing like this had
been published before. But then someone looked back at
Nash's PhD. dissertation, and discovered that Nash had
suggested this "mass action" interpretation way back around
1950 in his dissertation, but had never published it in a
journal article. All this and more is described in Nash's
Nobel prize seminar:

nobel.senashOpen ↗
lecture.html

In article <[email hidden]>,

Jim Menegay said:

When traditional game theorists first became aware of how
biology had reinterpreted the meaning of mixed strategies,
they considered this a major innovation - nothing like this
had been published before. But then someone looked back at
Nash's PhD. dissertation, and discovered that Nash had
suggested this "mass action" interpretation way back around
1950 in his dissertation, but had never published it in a
journal article. All this and more is described in Nash's
Nobel prize seminar:

nobel.senashOpen ↗
lecture.html

One should note, without diminishing the value of that
lecture, that the seminar involved talks by several other
people, and the material in question is described (well) by
Eric Van Damme, not by Nash himself.

--
Joe Felsenstein [email hidden]
Department of Genome Sciences and Department of
Biology, University of Washington, Box 357730, Seattle,
WA 98195-7730 USA