Mathematical Obsessions
Friday, May 20, 2011
“In many real-world games, however, such as the stock market, some players believe, incorrectly and overconfidently, that
the other participants are not doing as much thinking as they
themselves are.
In these situations, the players are not in equilibrium ...”
http://www.hss.caltech.edu/~camerer/NYU/06-CamererHoChong.pdf
There is an episode in the series Numb3rs (which talks about 0-step and 1-step thinkers. And the character in this tv series who is a genius mathematician says that u win in chess by making a move that makes your opponent think its obvious but it's really not. Based on my experience with chess games: lost and won, this statement is right on.
More from the academic paper referenced above:
"The CH model consists of iterative decision rules for players
doing k steps of thinking, and the frequency distribution f(k)
(assumed to be Poisson) of step k players. The iterative process
begins with “step 0” types who do not assume anything about
their opponents and merely choose according to some probability
distribution (for simplicity, we assume uniform). “Step k” thinkers assume that their opponents are distributed, according to a
normalized Poisson distribution, from step 0 to step k 1; that
is, they accurately predict the relative frequencies of players
doing fewer steps of thinking, but ignore the possibility that some
players may be doing as much or more. Step 2 players of the
beauty contest game, for example, assume the other players are a
combination of step 0 players (whose average guess is 50), and
step 1 players (who guess 2
⁄3 times 50)."
the other participants are not doing as much thinking as they
themselves are.
In these situations, the players are not in equilibrium ...”
http://www.hss.caltech.edu/~camerer/NYU/06-CamererHoChong.pdf
There is an episode in the series Numb3rs (which talks about 0-step and 1-step thinkers. And the character in this tv series who is a genius mathematician says that u win in chess by making a move that makes your opponent think its obvious but it's really not. Based on my experience with chess games: lost and won, this statement is right on.
More from the academic paper referenced above:
"The CH model consists of iterative decision rules for players
doing k steps of thinking, and the frequency distribution f(k)
(assumed to be Poisson) of step k players. The iterative process
begins with “step 0” types who do not assume anything about
their opponents and merely choose according to some probability
distribution (for simplicity, we assume uniform). “Step k” thinkers assume that their opponents are distributed, according to a
normalized Poisson distribution, from step 0 to step k 1; that
is, they accurately predict the relative frequencies of players
doing fewer steps of thinking, but ignore the possibility that some
players may be doing as much or more. Step 2 players of the
beauty contest game, for example, assume the other players are a
combination of step 0 players (whose average guess is 50), and
step 1 players (who guess 2
⁄3 times 50)."
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