From[Bill Williams 21 May 2004 3:40 PM CST]
I am updating Rick Marken's score card again as a result of his recent
posting. His score on the 28'th of April was minus 4, with the two recent
errors, I am now reporting a cumulative score of minus 6.
Bill Williams
[From Bill Powers (2004.05.21.1547 MDT)]
Bill Williams 21 May
2004 3:40 PM CST]I am updating Rick Marken’s score card again as a result of his
recentposting. His score on the 28’th of April was minus 4, with the two
recenterrors, I am now reporting a cumulative score of minus
6.
I found the appended definition of the Bellman Equation. You’re going to
have to explain to me what this has to do with control theory. I can’t
see any resemblance.
Bill P.
Glossary
from
Econterms
Definition: A Bellman equaion is any value or flow value equation. For a
discrete problem it can generally be of the form:
v(k) = max over k’ of { u(k,k’) + b*v(k’) }
where:
u() is the one-period return function (e.g., a utility function)
and
v() is the value function and
k is the current state and
k’ is the state to be chosen and
b is a scalar real parameter, the discount rate, generally slightly less
than
one.(Econterms)
From[Bill Williams 21 May 2004 10:20 PM CST]
[From Bill Powers (2004.05.21.1547 MDT)]
What you came up with is a description rather than a definition. When orthodox economic theorists realized that the principle of maximization didn’t have anything at all to say about a process involving time, they look about and hit upon the work of Richard Bellman who was a prominent control theorist. So, using the classical mathematical methods that Bellman used they came up with a hybrid system in which the principle of maximization provided the theory of value, and what they called the Bellman Equations provided the computational dynamics. So, now the orthodox theorists had a standard method that they could use to model an economy. Starting in a state of equilibrium they could subject the economy to an external shock and mathematically describe the path of the system through time.
However, Richard Bellman was a prominent control theorist, and thus there is control theory, a lot of control theory, already in economics. The difficulty, from my standpoint is that it is a patch upon and orthodoxy that assumes from first principles that behavior is a process of maximization and that control theory is merely a method to implement maximization. and all the rest of the stuff that comes with orthodox economics.
Bill Williams
From my point of view this work is of the character of, “If pigs could fly, what would be their lift to drag ratio?”
[From Bill Powers (2004.05.21.1547 MDT)]
Bill Williams 21 May 2004 3:40 PM CST] I am updating Rick Marken's score card again as a result of his recent posting. His score on the 28'th of April was minus 4, with the two recent errors, I am now reporting a cumulative score of minus 6.I found the appended definition of the Bellman Equation. You’re going to have to explain to me what this has to do with control theory. I can’t see any resemblance.
Bill P.
Definition of Bellman Equation
Glossary
from Econterms
Definition: A Bellman equaion is any value or flow value equation. For a discrete problem it can generally be of the form:v(k) = max over k’ of { u(k,k’) + b*v(k’) }
where:
u() is the one-period return function (e.g., a utility function) and
v() is the value function and
k is the current state and
k’ is the state to be chosen and
b is a scalar real parameter, the discount rate, generally slightly less than one.(Econterms)