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a Paradox in Game Theory: Losing Strategy That Wins

A recent discovery by a leading physicist 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.

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.

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." he said, "..it does not mean, however that it is simple and easy, just that it is counter-intuitive and possibly arduous in practice precisely because of its seeming implausibility."

The paradox may shed light on social interactions and voting behaviors. 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.

Two seemingly detrimental factors can result, under random or periodic alternation of their dynamics, in a winning game: “losing + losing = winning”. We at staylazy follow Parrondo’s paradox of combining different dynamics and we apply it to the case of three-dimensional quadratic 'negotiations', since virtually all negotiations are multidimensional (ie involve more factors than two people at the table). The fact is, it is a truism that better the negotiator you are, progressively more difficult to attain the same result, simply by virtue of your opposition being equally progressively prepared. We aim to prove that the periodic mixing of two chaotic dynamics originates an ordered dynamics in certain cases. This provides an explicit example of a different Parrondian paradoxical phenomenon: “stay + lazy = win”.

res ipsa loquitur (deeds speak for themselves).

Thank you for your consideration.

Sincerely Yours,

Lisa

Mary

Vanessa

Patricia

Maurice

David

Iva

... and the Staylazy Team.

staylazy.ca@gmail.com

paradox:

Main Entry: par·a·dox Pronunciation: 'par-&-"däksFunction: nounEtymology: Latin paradoxum, from Greek paradoxon, from neuter of paradoxos contrary to expectation, from para- + dokein to think, seem --1 : a tenet contrary to received opinion 2 a : a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true b : a self-contradictory statement that at first seems untrue c : an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises 3 : one that possesses seemingly contradictory qualities or phases.