Addendum to "Numerical Methods Disguised" (SIGNUM Newsletter, July 1986, 21: 31-32)

I regret the copy of "Numerical Methods Disguised" (SIGNUM Newsletter, July 1986, 21: 31-32) that I forwarded to you had the last paragraph omitted. It reads:An analytical solution of the same problem should also be presented. Thus for a seller's market, the compromise price will be B + (2/3)(S - B). The figure 2/3 is obtained by observing that the bargaining procedure uses successive halving. Hence the series 1 - 1/2+1/4 - 1/8+1/16 - 1/32+1/64 - ... which converges to 2/3. How close to 2/3 the compromise price will be depends on the tolerance, i.e., on how many terms in the series will be summed. Identical reasoning gives the compromise price in a buyer's market as B+(1/3)(S - B). Note that these expressions are algebraically identical to (2/3)S+(1/3)B and (1/3)S+(2/3)B respectively, which, in that form, nicely covey the idea behind a seller's or buyer's market.