[ExI] Ants for spike!
emlynoregan at gmail.com
Wed Nov 11 01:18:12 UTC 2009
2009/11/11 Keith Henson <hkeithhenson at gmail.com>:
> On Tue, Nov 10, 2009 at 4:00 AM, Emlyn wrote:
>> How can this be kin selection when none of the ants involved is able to breed?
>> I would think natural selection in ants is at the level of the nest,
>> not the individual; the individuals are more like cells in the body.
>> Or is this wrong?
> It's wrong. There is no logical way for biological evolution to take
> place at any level above the gene.
> This is the central dogma of St. Dawkins.
I understand all that. What I meant was, this isn't really kin
selection in the way it is meant in other species.
The reproduction of ants is at the nest level; it all funnels through
the fertile members (the queen and whichever male mates with her; is
it the same as bees?), these embody the germline of the nest.
The other ants are somatic cell equivalents. They are necessary, and
natural selection does indeed work on them of course, but not in the
manner of kin selection. There is a lot of maths around kin selection
(defining kin selection), around the genetic similarity between one
critter and another, which doesn't apply to worker ants.
Also, the equation here is not just risk in freeing a trapped ant
versus cost of losing that ant. Ants will behave in some way which
hopefully converges on the optimal solution to that equation, but
might be skewed for all kinds of reasons, not the least of which is
that the optimal solution may not be computable.
Seemingly unrelated but actually I think entirely on topic is this article:
What computer science can teach economics
November 9, 2009 by Larry Hardesty
(PhysOrg.com) -- Computer scientists have spent decades developing
techniques for answering a single question: How long does a given
calculation take to perform? Constantinos Daskalakis, an assistant
professor in MIT’s Computer Science and Artificial Intelligence
Laboratory, has exported those techniques to game theory, a branch of
mathematics with applications in economics, traffic management -- on
both the Internet and the interstate -- and biology, among other
things. By showing that some common game-theoretical problems are so
hard that they’d take the lifetime of the universe to solve,
Daskalakis is suggesting that they can’t accurately represent what
happens in the real world.
Game theory is a way to mathematically describe strategic reasoning —
of competitors in a market, or drivers on a highway or predators in a
habitat. In the last five years alone, the Nobel Prize in economics
has twice been awarded to game theorists for their analyses of
multilateral treaty negotiations, price wars, public auctions and
taxation strategies, among other topics.
In game theory, a “game” is any mathematical model that correlates
different player strategies with different outcomes. One of the
simplest examples is the penalty-kick game: In soccer, a penalty kick
gives the offensive player a shot on goal with only the goalie
defending. The goalie has so little reaction time that she has to
guess which half of the goal to protect just as the ball is struck;
the shooter tries to go the opposite way. In the game-theory version,
the goalie always wins if both players pick the same half of the goal,
and the shooter wins if they pick different halves. So each player has
two strategies — go left or go right — and there are two outcomes —
kicker wins or goalie wins.
It’s probably obvious that the best strategy for both players is to
randomly go left or right with equal probability; that way, both will
win about half the time. And indeed, that pair of strategies is what’s
called the “Nash equilibrium” for the game. Named for John Nash — who
taught at MIT and whose life was the basis for the movie A Beautiful
Mind — the Nash equilibrium is the point in a game where the players
have found strategies that none has the incentive to change
unilaterally. In this case, for instance, neither player can improve
her outcome by going one direction more often than the other.
Of course, most games are more complicated than the penalty-kick game,
and their Nash equilibria are more difficult to calculate. But the
reason the Nash equilibrium is associated with Nash’s name — and not
the names of other mathematicians who, over the preceding century, had
described Nash equilibria for particular games — is that Nash was the
first to prove that every game must have a Nash equilibrium. Many
economists assume that, while the Nash equilibrium for a particular
market may be hard to find, once found, it will accurately describe
the market’s behavior.
Daskalakis’s doctoral thesis — which won the Association for Computing
Machinery’s 2008 dissertation prize — casts doubts on that assumption.
Daskalakis, working with Christos Papadimitriou of the University of
California, Berkeley, and the University of Liverpool’s Paul Goldberg,
has shown that for some games, the Nash equilibrium is so hard to
calculate that all the computers in the world couldn’t find it in the
lifetime of the universe. And in those cases, Daskalakis believes,
human beings playing the game probably haven’t found it either.
In the real world, competitors in a market or drivers on a highway
don’t (usually) calculate the Nash equilibria for their particular
games and then adopt the resulting strategies. Rather, they tend to
calculate the strategies that will maximize their own outcomes given
the current state of play. But if one player shifts strategies, the
other players will shift strategies in response, which will drive the
first player to shift strategies again, and so on. This kind of
feedback will eventually converge toward equilibrium: in the
penalty-kick game, for example, if the goalie tries going in one
direction more than half the time, the kicker can punish her by always
going the opposite direction. But, Daskalakis argues, feedback won’t
find the equilibrium more rapidly than computers could calculate it.
The argument has some empirical support. Approximations of the Nash
equilibrium for two-player poker have been calculated, and
professional poker players tend to adhere to it — particularly if
they’ve read any of the many books or articles on game theory’s
implications for poker. The Nash equilibrium for three-player poker,
however, is intractably hard to calculate, and professional poker
players don’t seem to have found it.
How can we tell? Daskalakis’s thesis showed that the Nash equilibrium
belongs to a set of problems that is well studied in computer science:
those whose solutions may be hard to find but are always relatively
easy to verify. The canonical example of such a problem is the
factoring of a large number: The solution seems to require trying out
lots of different possibilities, but verifying an answer just requires
multiplying a few numbers together. In the case of Nash equilibria,
however, the solutions are much more complicated than a list of prime
numbers. The Nash equilibrium for three-person Texas hold ’em, for
instance, would consist of a huge set of strategies for any possible
combination of players’ cards, dealers’ cards, and players’ bets.
Exhaustively characterizing a given player’s set of strategies is
complicated enough in itself, but to the extent that professional
poker players’ strategies in three-player games can be characterized,
they don’t appear to be in equilibrium.
Anyone who’s into computer science — or who read “Explained: P vs. NP”
on the MIT News web site last week — will recognize the set of
problems whose solutions can be verified efficiently: It’s the set
that computer scientists call NP. Daskalakis proved that the Nash
equilibrium belongs to a subset of NP consisting of hard problems with
the property that a solution to one can be adapted to solve all the
others. (The cognoscenti will infer that it’s the set called
NP-complete; but the fact that the Nash equilibrium always exists
disqualifies it from NP-completeness. In fact, it belongs to a
different set, called PPAD-complete.)
That result “is one of the biggest yet in the roughly 10-year-old
field of algorithmic game theory,” says Tim Roughgarden, an assistant
professor of computer science at Stanford University. It “formalizes
the suspicion that the Nash equilibrium is not likely to be an
accurate predictor of rational behavior in all strategic
Given the Nash equilibrium’s unreliability, says Daskalakis, “there
are three routes that one can go. One is to say, We know that there
exist games that are hard, but maybe most of them are not hard.” In
that case, Daskalakis says, “you can seek to identify classes of games
that are easy, that are tractable.”
The second route, Daskalakis says, is to find mathematical models
other than Nash equilibria to characterize markets — models that
describe transition states on the way to equilibrium, for example, or
other types of equilibria that aren’t so hard to calculate. Finally,
he says, it may be that where the Nash equilibrium is hard to
calculate, some approximation of it — where the players’ strategies
are almost the best responses to their opponents’ strategies — might
not be. In those cases, the approximate equilibrium could turn out to
describe the behavior of real-world systems.
As for which of these three routes Daskalakis has chosen, “I’m
pursuing all three,” he says.
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