Recall the game between R and D determined by the following data.
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
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.
- Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK. Republished by Methuen and Company, London, UK, 1964. Online.
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.
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