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We model the commercial World Wide Web as a directed graph emerging as the equilibrium of a game in which utility maximizing Web sites purchase (advertising) in-links from each other, while also setting the price of these links. In equilibrium, higher content sites tend to purchase more advertising links (mirroring the Dorfman-Steiner rule) while selling(More)
We study the diffusion process in an online social network given the individual connections between members. We model the adoption decision of individuals as a binary choice affected by three factors: (1) the local network structure formed by already adopted neighbors, (2) the average characteristics of adopted neighbors (influencers), and (3) the(More)
A dening property of the World Wide Web is a content site's ability to place virtually costless hyperlinks to third-party content as a substitute or complement to its own content. Costless hyper-linking has enabled new types of players, usually referred to as content aggregators, to successfully enter content ecosystems, attracting trac and revenue by(More)
Let F be a family of an n-element set. It is called intersecting if every pair of its members have a non-disjoint intersection. It is well-known that an intersecting family satisfies the inequality |F| ≤ 2 n−1. Suppose that |F| = 2 n−1 +i. Choose the members of F independently with probability p (delete them with probability 1 − p). The new family is(More)
Paid placements on search engines reached sales of over $10 billion in the U.S. last year and represent the most rapidly growing form of online advertising today. In its classic form, a search engine sets up an auction for each search word in which competing web sites bid for their sponsored links to be displayed next to the search results. We model this(More)
Web sites invest significant resources in trying to influence their visibility among online search results. In addition to paying for sponsored links, they invest in methods known as search engine optimization (SEO) that improve the ranking of a site among the search results without improving its quality. We study the economic incentives of Web sites to(More)
Consider the following modification of the Barabási–Albert random graph. At every step a new vertex is added to the graph. It is connected to the old vertices randomly, with probabilities proportional to the degree of the other vertex, and independently of each other. We show that the proportion of vertices of degree k decreases at the rate of k −3.(More)
Let [n] denote the set {1, 2, ..., n}, 2 [n] the collection of all subsets of [n] and F ⊂ 2 [n] be a family. The maximum of |F | is studied if any r subsets have an at least s-element intersection and there are no subsets containing t + 1 common elements. We show that |F| ≤ € t−s i=0 n−s i ¡ + t+−s t+2−s n−s t+1−s ¡ + − 2 and this bound is asymptotically(More)
Let H denote the set {f 1 , f 2 , ..., f n }, 2 [n] the collection of all subsets of H and F ⊆ 2 [n] be a family. The maximum of |F| is studied if any k subsets have a non-empty intersection and the intersection of any l distinct subsets (1 ≤ k < l) is empty. This problem is reduced to a covering problem. If we have the conditions that any two subsets have(More)