Modeling self-organization of communication and topology in social networks

This paper introduces a model of self-organization between communication and topology in social networks, with a feedback between different communication habits and the topology. To study this feedback, we let agents communicate to build a perception of a network and use this information to create strategic links. We observe a narrow distribution of links when the communication is low and a system with a broad distribution of links when the communication is high. We also analyze the outcome of chatting, cheating, and lying, as strategies to get better access to information in the network. Chatting, although only adopted by a few agents, gives a global gain in the system. Contrary, a global loss is inevitable in a system with too many liarsComment: 6 pages 7 figures, Java simulation available at http://cmol.nbi.dk/models/inforew/inforew.htm

Analysis of a continuous-time model of structural balance

It is not uncommon for certain social networks to divide into two opposing camps in response to stress. This happens, for example, in networks of political parties during winner-takes-all elections, in networks of companies competing to establish technical standards, and in networks of nations faced with mounting threats of war. A simple model for these two-sided separations is the dynamical system dX/dt = X^2 where X is a matrix of the friendliness or unfriendliness between pairs of nodes in the network. Previous simulations suggested that only two types of behavior were possible for this system: either all relationships become friendly, or two hostile factions emerge. Here we prove that for generic initial conditions, these are indeed the only possible outcomes. Our analysis yields a closed-form expression for faction membership as a function of the initial conditions, and implies that the initial amount of friendliness in large social networks (started from random initial conditions) determines whether they will end up in intractable conflict or global harmony.Comment: 12 pages, 2 figure

Truthful Mechanisms with Implicit Payment Computation

It is widely believed that computing payments needed to induce truthful bidding is somehow harder than simply computing the allocation. We show that the opposite is true: creating a randomized truthful mechanism is essentially as easy as a single call to a monotone allocation rule. Our main result is a general procedure to take a monotone allocation rule for a single-parameter domain and transform it (via a black-box reduction) into a randomized mechanism that is truthful in expectation and individually rational for every realization. The mechanism implements the same outcome as the original allocation rule with probability arbitrarily close to 1, and requires evaluating that allocation rule only once. We also provide an extension of this result to multi-parameter domains and cycle-monotone allocation rules, under mild star-convexity and non-negativity hypotheses on the type space and allocation rule, respectively. Because our reduction is simple, versatile, and general, it has many applications to mechanism design problems in which re-evaluating the allocation rule is either burdensome or informationally impossible. Applying our result to the multi-armed bandit problem, we obtain truthful randomized mechanisms whose regret matches the information-theoretic lower bound up to logarithmic factors, even though prior work showed this is impossible for truthful deterministic mechanisms. We also present applications to offline mechanism design, showing that randomization can circumvent a communication complexity lower bound for deterministic payments computation, and that it can also be used to create truthful shortest path auctions that approximate the welfare of the VCG allocation arbitrarily well, while having the same running time complexity as Dijkstra's algorithm.Comment: This is a full version of the conference paper from ACM EC 2010, merged with a multi-parameter extension (Section 8) from the follow-up paper in ACM EC 2013 by the same authors. Apart from the revised presentation, this version is updated to reflect the follow-up work and the current status of open questions. The current version (v5) contains several minor bug fixes in the proof of Lemma 7.10. J. of the ACM (JACM), Volume 62, Issue 2, May 201

Prophet Inequalities with Limited Information

In the classical prophet inequality, a gambler observes a sequence of stochastic rewards $V_1,...,V_n$ and must decide, for each reward $V_i$, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value $V_i$. The gambler's goal is to obtain a constant fraction of the expected reward that the optimal offline algorithm would get. Recently, prophet inequalities have been generalized to settings where the gambler can choose $k$ items, and, more generally, where he can choose any independent set in a matroid. However, all the existing algorithms require the gambler to know the distribution from which the rewards $V_1,...,V_n$ are drawn. The assumption that the gambler knows the distribution from which $V_1,...,V_n$ are drawn is very strong. Instead, we work with the much simpler assumption that the gambler only knows a few samples from this distribution. We construct the first single-sample prophet inequalities for many settings of interest, whose guarantees all match the best possible asymptotically, \emph{even with full knowledge of the distribution}. Specifically, we provide a novel single-sample algorithm when the gambler can choose any $k$ elements whose analysis is based on random walks with limited correlation. In addition, we provide a black-box method for converting specific types of solutions to the related \emph{secretary problem} to single-sample prophet inequalities, and apply it to several existing algorithms. Finally, we provide a constant-sample prophet inequality for constant-degree bipartite matchings. We apply these results to design the first posted-price and multi-dimensional auction mechanisms with limited information in settings with asymmetric bidders

Simple and Near-Optimal Mechanisms For Market Intermediation

A prevalent market structure in the Internet economy consists of buyers and sellers connected by a platform (such as Amazon or eBay) that acts as an intermediary and keeps a share of the revenue of each transaction. While the optimal mechanism that maximizes the intermediary's profit in such a setting may be quite complicated, the mechanisms observed in reality are generally much simpler, e.g., applying an affine function to the price of the transaction as the intermediary's fee. Loertscher and Niedermayer [2007] initiated the study of such fee-setting mechanisms in two-sided markets, and we continue this investigation by addressing the question of when an affine fee schedule is approximately optimal for worst-case seller distribution. On one hand our work supplies non-trivial sufficient conditions on the buyer side (i.e. linearity of marginal revenue function, or MHR property of value and value minus cost distributions) under which an affine fee schedule can obtain a constant fraction of the intermediary's optimal profit for all seller distributions. On the other hand we complement our result by showing that proper affine fee-setting mechanisms (e.g. those used in eBay and Amazon selling plans) are unable to extract a constant fraction of optimal profit in the worst-case seller distribution. As subsidiary results we also show there exists a constant gap between maximum surplus and maximum revenue under the aforementioned conditions. Most of the mechanisms that we propose are also prior-independent with respect to the seller, which signifies the practical implications of our result.Comment: To appear in WINE'14, the 10th conference on Web and Internet Economic

Degree Distribution of Competition-Induced Preferential Attachment Graphs

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment random graph models with upper cutoffs. This is the first explanation of how preferential attachment can arise from a more basic underlying mechanism of local competition. We rigorously determine the degree distribution for the family of random graph models, showing that it obeys a power law up to a finite threshold and decays exponentially above this threshold. We also rigorously analyze a generalized version of our graph process, with two natural parameters, one corresponding to the cutoff and the other a ``fertility'' parameter. We prove that the general model has a power-law degree distribution up to a cutoff, and establish monotonicity of the power as a function of the two parameters. Limiting cases of the general model include the standard preferential attachment model without cutoff and the uniform attachment model.Comment: 24 pages, one figure. To appear in the journal: Combinatorics, Probability and Computing. Note, this is a long version, with complete proofs, of the paper "Competition-Induced Preferential Attachment" (cond-mat/0402268

Social Ranking Techniques for the Web

The proliferation of social media has the potential for changing the structure and organization of the web. In the past, scientists have looked at the web as a large connected component to understand how the topology of hyperlinks correlates with the quality of information contained in the page and they proposed techniques to rank information contained in web pages. We argue that information from web pages and network data on social relationships can be combined to create a personalized and socially connected web. In this paper, we look at the web as a composition of two networks, one consisting of information in web pages and the other of personal data shared on social media web sites. Together, they allow us to analyze how social media tunnels the flow of information from person to person and how to use the structure of the social network to rank, deliver, and organize information specifically for each individual user. We validate our social ranking concepts through a ranking experiment conducted on web pages that users shared on Google Buzz and Twitter.Comment: 7 pages, ASONAM 201

A fitness model for the Italian Interbank Money Market

We use the theory of complex networks in order to quantitatively characterize the formation of communities in a particular financial market. The system is composed by different banks exchanging on a daily basis loans and debts of liquidity. Through topological analysis and by means of a model of network growth we can determine the formation of different group of banks characterized by different business strategy. The model based on Pareto's Law makes no use of growth or preferential attachment and it reproduces correctly all the various statistical properties of the system. We believe that this network modeling of the market could be an efficient way to evaluate the impact of different policies in the market of liquidity.Comment: 5 pages 5 figure

Kronecker Graphs: An Approach to Modeling Networks

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models either fail to match several of the above properties, are complicated to analyze mathematically, or both. In this paper we propose a generative model for networks that is both mathematically tractable and can generate networks that have the above mentioned properties. Our main idea is to use the Kronecker product to generate graphs that we refer to as "Kronecker graphs". First, we prove that Kronecker graphs naturally obey common network properties. We also provide empirical evidence showing that Kronecker graphs can effectively model the structure of real networks. We then present KronFit, a fast and scalable algorithm for fitting the Kronecker graph generation model to large real networks. A naive approach to fitting would take super- exponential time. In contrast, KronFit takes linear time, by exploiting the structure of Kronecker matrix multiplication and by using statistical simulation techniques. Experiments on large real and synthetic networks show that KronFit finds accurate parameters that indeed very well mimic the properties of target networks. Once fitted, the model parameters can be used to gain insights about the network structure, and the resulting synthetic graphs can be used for null- models, anonymization, extrapolations, and graph summarization