As long as various Mongo's continue to assert that narrow self-interest is
the sole motivator of rational behavior, thoughtful cypherpunks may not
take this issue and the related economic analysis seriously.
...So we must fly a rebel flag
As others did before us,
And we must sing a rebel song
And join in rebel chorus.
We'll make the tyrants feel the sting
O'those that they would throttle;
They needn't say the fault is ours
If blood should stain the wattle
�It seems somewhat ridiculous to talk of revolution . . .
But everything else is even more ridiculous, since it
implies accepting the existing order in one way or
another.�
� Situationist International #1
By SANDRA BLAKESLEE
Spanish physicist has discovered what appears to be a new law of nature
that may help explain, among other things, how life arose out of a
primordial soup, why President Clinton's popularity rose after he was
caught in a sex scandal, and why investing in losing stocks can sometimes
lead to greater capital gains.
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Unfortunately, these tactics won't work at the casino.
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Called Parrondo's paradox, the law states that two games guaranteed to make
a player lose all his money will generate a winning streak if played
alternately.
Named after its discoverer, Dr. Juan Parrondo, who teaches physics at the
Complutense University in Madrid, the newly discovered paradox is inspired
by the mechanical properties of ratchets -- the familiar saw-tooth tools
used to lift automobiles and run self-winding wristwatches. By translating
the properties of a ratchet into game theory -- a relatively new scientific
discipline that seeks to extract rules of nature from the gains and losses
observed in games -- Dr. Parrondo discovered that two losing games could
combine to increase one's wealth.
"The importance of the paradox in real life remains to be seen," said Dr.
Charles Doering, a mathematician at the University of Michigan, who is
familiar with the research. "It gives us a new and unexpected view of a
variety of phenomena," he said, "and who knows? Sometimes finding that one
piece of the puzzle makes the whole picture suddenly clear."
Dr. Derek Abbott, director of the Center for Biomedical Engineering at the
University of Adelaide in Australia, said that many scientists were
intrigued by the paradox and had begun applying it to engineering,
population dynamics, financial risk and other disciplines.
Dr. Abbott and a colleague at his center, Dr. Gregory Harmer, recently
carried out experiments to verify and explain how Parrondo's paradox works.
Their research is described in the Dec. 23 issue of Nature.
The paradox is illustrated by two games played with coins weighted on one
side so that they will not fall evenly by chance to heads or tails.
In game A, a player tosses a single loaded coin and bets on each throw. The
probability of winning is less than half. In game B, a player tosses one of
two loaded coins with a simple rule added. He plays Coin 1 if his money is
a multiple of a particular whole number, like three.
If his money cannot be divided by the number three, he plays the Coin 2. In
this setup, the second will be played more often than the first.
Both are loaded, one to lose badly and one to win slightly, with the upshot
being that anyone playing this game will eventually lose all his money.
"Sure enough," Dr. Abbott said, when a person plays either game 100 times,
all money taken to the gambling table is lost. But when the games are
alternated -- playing A twice and B twice for 100 times -- money is not lost.
It accumulates into big winnings. Even more surprising, he said, when game
A and B are played randomly, with no order in the alternating sequence,
winnings also go up and up.
This is Parrondo's paradox. Switching between the two games creates a
ratchet-like effect. With its saw-tooth shape, a ratchet allows movement in
one direction and blocks it in the other.
"You see ratchets everywhere in life," Dr. Abbott said. "Any child knows
that when you shake a bag of mixed nuts, the Brazil nuts rise to the top.
This is because smaller nuts block downward movement of larger nuts." This
trapping of heavier objects -- moving them upward when one would expect
them to fall down -- is the essence of a ratchet.
The same is true for particles that tend to move randomly within cells but
can be captured, or ratcheted, into performing useful work. This is how
many proteins and enzymes are designed, Dr. Abbott said.
Sharing an interest in microscopic ratchets, Dr. Abbott and Dr. Parrondo
met in a coffee shop in Madrid in 1997 to discuss the phenomenon. They
started to wonder what might happen with a so-called flashing ratchet.
First, they imagined two tilted slopes that could be laid on top of each
other or held apart.
One is smooth and straight, the other saw-toothed.
Particles placed at the top of either slope would fall down to the bottom
under the pull of gravity. Particles placed at the bottom of either slope
would go nowhere.
But if the two slopes were superimposed and alternated or "flashed" back
and forth, particles resting at the bottom could be made to move uphill.
Dr. Parrondo then translated a flashing ratchet into the language of game
theory. Then, he devised the two coin games that Dr. Abbott confirmed in
recent experiments. Game A is like the smooth slope. The single loaded coin
produces steady losses, just like particles sliding straight downhill. Game
B is like the saw-tooth slope that can catch objects. Each tooth on a
ratchet has two sides, one that goes up and one that goes down.
The two coins, one good and one bad, are like two sides of a single
saw-tooth. In a computer, the games are played 100 times, mimicking a
ratchet with many teeth.
Each winning round carries the player's money uphill, Dr. Abbott said.
Capital starts accumulating, just like particles moving up the slope of the
flashing ratchet. Switching the game traps the money before new rounds of
the game cause the money to be lost.
Unfortunately, Parrondo's paradox will not work for the kinds of games
played in casinos, Dr. Abbott said.
Games A and B must be set up to copy a ratchet, which means they must have
some direct interaction. In the experiments carried out by Dr. Abbott, game
B depends on the amount of capital being played and game A affects those
amounts.
They are subtly connected, he said.
Parrondo's paradox may help scientists find new ways to separate molecules,
design tiny motors and understand games of survival being played at the
level of individual genes.
Life itself may have been bootstrapped by ratchets, Dr. Abbott said. When
simple amino acids were formed by chance, environmental forces would tend
to destroy incipient order. Ratchets could help move life along its
evolutionary pathways toward greater complexity.
Economists are studying Parrondo's paradox to help find the best strategies
for managing investments. Dr. Sergei Maslov, a physicist at Brookhaven
National Laboratory in Upton, N.Y., recently showed that if an investor
simultaneously shared capital between two losing stock portfolios, capital
would increase rather than decrease.
"It's mind-boggling," Dr. Maslov said.
"You can turn two minuses into a plus." But so far, he said, it is too
early to apply his model to the real stock market because of its complexity.
The paradox may shed light on social interactions and voting behaviors, Dr.
Abbott said. For example, President Clinton, who at first denied having a
sexual affair with Monica S. Lewinsky (game A) saw his popularity rise when
he admitted that he had lied (game B.) The added scandal created more good
for Mr. Clinton.
http://seneca.fis.ucm.es/parr/GAMES/Paradox%20in%20Game%20Theory%20Losing%20Strategy%20That%20Wins.htm
