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Sunday, June 2, 2013
Does The Nash Equilibrium Apply To Open Water Racing?
Most definitely not, but what if he did?
In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally.
If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
This seems to be the case in elite competitive open water swimming where a pack of swimmers are typically in Nash equilibrium for much of the race until the end.
In a pack, each swimmer is individually making the best decision that he or she can, taking into account the strategic decisions of the others (i.e., stay in the pack). Occasionally, a swimmer may make a surge or a position move during the race that temporarily upsets the equilibrium, but typically the overwhelming propensity for equilibrium overcomes the tendency for one swimmer to make a break.
However, this equilibrium rapidly breaks down in the last 30% of the race when the more fit swimmers start to execute their own individual decisions based on their fundamental desire to win. These various subgame perfect equilibria, created by individual swimmers due to their desire to win, completely breaks down the ongoing Nash equilibrium. And like Ous Mellouli who broke away during the last 30% of the Olympic 10K Marathon Swim at the 2012 London Olympic Games, Nash equilibrium is rapidly destroyed and the race to the finish takes on the best response strategy.
Copyright © 2013 by Open Water Swimming
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Open Water Swimming MagazineThe Open Water Swimming Magazine is the monthly magazine entirely focused on open water swimming heroes and heroines of every age, ability, and background. Published by the World Open Water Swimming Association, the Open Water Swimming Magazine is a free benefit to WOWSA members.
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2014 Open Water Swimming Almanac
An Almanac for Open Water SwimmingAn almanac is essentially a body of knowledge which is so complete that it enables people in different fields to make predictions about the future of their respective industries.
This, for example, was the purpose of the traditional farmers almanacs. It enabled farmers to determine as accurately as possible which crops to plant for the greatest harvests in a given year.
But the farmers almanac was just one example among many.
There are, of course, many different kinds of almanacs.
In fact, there is even one for open water swimming...
Preview the Open Water Swimming Almanac:
The trends are very clear.
The tide is rising for open water swimming.