1. Tilke, Max, or Karl Max
2. if ? 0 (g) ? ? * (g ), independently from the value of c, given c < ?. On the other hand;Therefore, ? * (g) ? ? * (g )
3. ) for all i, j in S, d (i, j; g) ? k, and (2) for all i not in S there is a consumer j in S such that d (i, j; g) < k. Since g ? g, d (i, j; g) ? d (i, j; g ) for all i, j in N and, in particular, for all i, j in S. But then (1) implies that for all i, j in S d (i, j; g ) ? k. If for all i not in S, there is a j in S such that d (i, j; g ) < k, then S ? N k (g ). But, if this is not true, then there exist an i not in S such that for all j in S, the distance d (i, j; g ) ? k. Take?STake? Take?S = (S ? i) ? S. It could be that either?Seither? either?S ? N k (g ), or that there exists an h not i� S such that for all j i� S, d (h, j; g ) ? k. Then, I add this consumer h to the set S. Eventually, I would continue adding consumers to the set S until the condition (2) for S is satisfied. Therefore, there exists an S ? N k (g ) such that S ? S . This completes the proof of Claim. Since argmax S?N k (g) |S| ? N k (g), then, by the claim, there exists a� S in N k (g ) such that argmax S?N k (g) |S| ? ? S. By definition, | ? S| ? max S ?N k (g ) |S |, and therefore;|s| ; G;there exists an S ? N k (g ) such that S ? S . Proof of Claim. By definition of N k (g), if S is in N k (g), then
4. Role of Product-Related Conversations in the Diffusion of a New Product;J Arndt;Journal of Marketing Research,1967