|
|
|
|
|
|
|
loss (negative of the payoff) the opponent can impose. It is interesting that often (checkers, chess, go) this minimax strategy is a pure strategy. Thus, although the payoff may vary on successive trials of the same strategy, the plan can still restrict its search to pure strategies in such cases. In more general situations, however, the plan will have to employ stochastic mixtures of pure strategies and, if it is to exploit its opponents maximally, it will even associate particular mixtures with particular kinds of opponents (assuming it is supplied with enough information to enable it to identify individual opponents). |
|
|
|
|
|
|
|
|
Considered in the  framework, the strategies become the elements of the domain of action  and the plans for employing these strategies become elements of  . The set of admissible environments e depends upon the particular case considered. If it is known that the opponent has chosen a single pure strategy, then the set of admissible environments e is given by the set of pure strategies. The criterion  for ranking the plans is then built up from the unique payoff determined by each pair of opposing pure strategies, the example given being the ''gambler's ruin" criterion |
|
|
|
|
|
|
|
|
In the more complicated cases, the set of environments is enlarged, ultimately including plans over ; however, the accumulation functions Ut,E(t) are still defined and criteria such as the "gambler's ruin" criterion can still be used to rank the plans in . |
|
|
|
|
|
|
|
|
Once again, as in the previous two illustrations, the large size of and the complex relation of its elements to performance constitute a major barrier to improvement. Section 7.3 specifically discusses the role of adaptive algorithms in game strategy spaces defined in the manner of Samuel. In addition, the necessity of using non-payoff information generated during the play of more complex games presents special difficulties. This latter problem is addressed in section 8.4 as an elaboration of the concepts and techniques developed in the earlier chapters. |
|
|
|
 |
|
|
|
|
Summarizing: |
|
|
|
|
|
|
|
|
, strategies for the game. |
|
|
|
|
|
|
|
|
W,dependent upon the way strategies are represented; genetic operators will function if descriptors are used so that each strategy is designated by a string of descriptor values (see the predictive modeling technique of the next section for suggestions concerning operations on the strategy during the play; section 8.4 extends these ideas). |
|
|
|
|
|
|
|
|
, plans for testing strategies. |
|
|
|
|
|
