Combinatorial games

The principle of this simple combinatorial game is obvious by now it can be easily extended using other hydrocarbon building blocks. The three-membered ring, for example, can be enlarged and also be anchored to other positions of the allene element, of course, thus yielding ring structures such as 36-39. However, these will not be discussed comprehensively in this Chapter to keep its limits acceptable. Besides, cycloallenes (36) are dealt with separately in Chapter 6. 

Returning now to the theme of combinatorial games, the problems mentioned are sufficient for introducing the essential idea of metabolic optimization, and looking at the pentose phosphate pathway in the fight of it. First I shall treat this pathway as the game defmed in Figure 5.2, but afterwards we shall see how the apparently arbitrary rules actually apply to the real biochemical situation. 

Let us now express the solution to the combinatorial game in terms of the real biochemical problem in effect, we found that we could accomplish the conversion of three pentoses into two hexoses and one triose by the following steps ... 

R Holzman, N Kfir-Dahav, D Monderer, and M Tennenholtz. Bundling equilibrium in combinatorial auctions. Games and Economic Behavior, 2001. 

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