6. SOLUTIONS OF GAMES BY DIFFERENTIAL EQUATIONS
Gerald W. Brown, John von Neumann · Princeton University Press eBooks · 1951
Abstract : A new proof for the existence of a value and of good strategies for a zero-sum two-person game is given. This proof seems to have some interest because of two distinguishing traits: (a) although the theorem to be proved is of an algebraical nature, a very simple proof obtains by analytical means; and (b) the proof is constructive in a sense that lends itself to utilization when actually computing the solutions of specific games. The procedure could be mechanized with relative ease, both for digital and for analogy methods. In the latter case it is probably much less sensitive to the precision of the equipment, than the somewhat related problem of linear equation solving or matrix inversion.