A variation in the Brown method of solving games.

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Author
Jauregui, Stephen Jr.
Date
1960Advisor
Pulliam, F.M.
Campbell, Richard C.
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Show full item recordAbstract
The brown method of solving zero sum two person games
by a method of successive approximations was programmed for
the NCR-102A Digital Computer. Game matricies up to order
8x8 were investigated, although the program could easily be
extended to order 16 x 16 without leaving the magnetic drum,
or to arbitrarily higher order games by also using magnetic
tape. The problem of obtaining all strategies of a convex
set of optimal strategies was solved in a number of cases and
the concept of a complementary game was developed.
The Brown method was found to converge too slowly in
most cases so that a modification of the method was used. In
the Brown method, successive approximate strategies are developed
for each player until a stage is reached in which the
opposing strategies give equal values to the game (or give
values sufficiently close), at which time (approximate) optimal
strategies have been obtained. Julia Robinson has proved
the convergence of the Brown method. The modification consists
in comparing a maximum value of the game for Player I
with a minimum value of the game for Player II at different
stages of the iteration until these values are equal or
sufficiently close to each other. The convergence of the new
method follows from the convergence of the brown method and
the new method was found to be generally much more rapid.
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