## Forgetfulness Of Purpose • 5

Recall the game between R and D determined by the following data.

$\begin{array}{cc|ccc} \multicolumn{5}{c}{\text{Table 11/3/1}} \\[4pt] & & & R & \\ & & \alpha & \beta & \gamma \\ \hline & 1 & b & a & c \\ D & 2 & a & c & b \\ & 3 & c & b & a \end{array}$

Here is Ashby’s analysis of how it plays out.

Examination of the table soon shows that with this particular table R can win always.  Whatever value D selects first, R can always select a Greek letter that will give the desired outcome.  Thus if D selects 1, R selects β;  if D selects 2, R selects α;  and so on.  In fact, if R acts according to the transformation

$\begin{array}{cccc} & 1 & 2 & 3 \\ \downarrow & & & \\ & \beta & \alpha & \gamma \end{array}$

then he can always force the outcome to be a.

R‘s position, with this particular table, is peculiarly favourable, for not only can R always force a as the outcome, but he can as readily force, if desired, b or c as the outcome.  R has, in fact, complete control of the outcome.

### Reference

• Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.
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### 2 Responses to Forgetfulness Of Purpose • 5

1. As a game, it becomes a little (but only a little) more interesting when R&D make their selections in ignorance of the other’s choice. From my brief glance, it looks like (under those constraints) a random choice matrix becomes the only one that “works” for both, where “works” means provides any chance of breaking even. But my intuitions on such things are demonstrably crappy, so I look forward to the next entry.