[PDF] A Dynamic Model Of Network Formation With Strategic Interactions eBook

Author : Esteban Daniel Arcaute Aizpuru
Publisher :
Page : pages
File Size : 12,33 MB
Release : 2009
Category :
ISBN :

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Modern communication networks operate at a scale that makes the use of centralized policies/protocols challenging. At the same time, nodes in the network are self-interested strategic agents. It is therefore natural to model the formation of modern communication networks as the result of interactions between self-interested agents; and to consider the observed networks as its equilibrium outcomes. The aim of such modeling is to predict some macroscopic observable, here efficiency. If we want to make the best prediction possible, how should one model the strategic interactions of the agents, and what equilibrium concept should be used? In this thesis, we assume the network is the outcome of a network formation game. The network formation game considered captures two conflicting objectives of self-interested nodes in a network. On one hand, such a node wishes to be able to reach all other nodes in the network; on the other hand, it wishes to minimize its cost of participation. We focus on myopic local best response dynamics for such games, where nodes can only deviate to form links with others in a restricted neighborhood. For two general classes of costs of participating in the network, we show that a static analysis of the network formation game does not provide useful predictions about efficiency. To do so, we identify extrema outcomes, with respect to efficiency, in the equilibrium set and show they correspond to the extrema of all reasonable outcomes. In some cases, this holds true even when using strong stability as equilibrium concept. In terms of efficiency loss, we show the efficiency loss can be linear in the number of nodes. We then show that, for myopic local best response dynamics, if we allow a single node a "one step look-ahead'', the dynamics converge almost surely, and the efficiency loss can be constant. In some cases, our dynamics converge to efficient outcomes. Thus the prediction about efficiency can be as precise as possible, with one unique value predicted, and full efficiency achieved.

Author : Bhaskar Dutta
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 41,21 MB
Release : 2013-03-09
Category : Business & Economics
ISBN : 3540247904

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When Murat Sertel asked us whether we would be interested in organizing a special issue of the Review of Economic Design on the formation of networks and groups, we were happy to accept because of the growing research on this important topic. We were also pleasantly surprised at the response to our request for submissions to the special issue, receiving a much larger number of sub missions than we had anticipated. In the end we were able to put together two special issues of insightful papers on this topic. Given the growing interest in this topic, we also decided (with encouragement from Murat) to combine the special issues in the form of a book for wider dissemination. However, once we had decided to edit the book, it was natural to move beyond the special issue to include at least some of the papers that have been influential in the literature on the formation of networks. These papers were published in other journals, and we are very grateful to the authors as well as the journals for permission to include these papers in the book.

Author : Frank H. Page
Publisher :
Page : 0 pages
File Size : 37,33 MB
Release : 2009
Category :
ISBN :

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In all social and economic interactions, individuals or coalitions choose not only with whom to interact but how to interact, and over time both the structure (the "with whom") and the strategy ("the how") of interactions change. Our objectives here are to model the structure and strategy of interactions prevailing at any point in time as a directed network and to address the following open question in the theory of social and economic network formation: given the rules of network and coalition formation, the preferences of individuals over networks, the strategic behavior of coalitions in forming networks, and the trembles of nature, what network and coalitional dynamics are likely to emergence and persist. Our main contributions are (i) to formulate the problem of network and coalition formation as a dynamic, stochastic game, (ii) to show that this game possesses a stationary correlated equilibrium (in network and coalition formation strategies), (iii) to show that, together with the trembles of nature, this stationary correlated equilibrium determines an equilibrium Markov process of network and coalition formation which respects the rules of network and coalition formation and the preferences of individuals, and (iv) to show that, although uncountably many networks may form, this endogenous process of network and coalition formation possesses a nonempty finite set of ergodic measures and generates a finite, disjoint collection of nonempty subsets of networks and coalitions, each constituting a basin of attraction. Moreover, we extend to the setting of endogenous Markov dynamics the notions of pairwise stability (Jackson-Wolinsky, 1996), strong stability (Jackson-van den Nouweland, 2005), and Nash stability (Bala-Goyal, 2000), and we show that in order for any network-coalition pair to be stable (pairwise, strong, or Nash) it is necessary and sufficient that the pair reside in one of finitely many basins of attraction - and hence reside in the support of an ergodic measure. The results we obtain here for endogenous network dynamics and stochastic basins of attraction are the dynamic analogs of our earlier results on endogenous network formation and strategic basins of attraction in static, abstract games of network formation (Page and Wooders, 2008), and build on the seminal contributions of Jackson and Watts (2002), Konishi and Ray (2003), and Dutta, Ghosal, and Ray (2005).

Author : Bryan Graham
Publisher : Academic Press
Page : 244 pages
File Size : 19,15 MB
Release : 2020-06-03
Category : Business & Economics
ISBN : 0128117710

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The Econometric Analysis of Network Data serves as an entry point for advanced students, researchers, and data scientists seeking to perform effective analyses of networks, especially inference problems. It introduces the key results and ideas in an accessible, yet rigorous way. While a multi-contributor reference, the work is tightly focused and disciplined, providing latitude for varied specialties in one authorial voice. Answers both 'why' and 'how' questions in network analysis, bridging the gap between practice and theory allowing for the easier entry of novices into complex technical literature and computation Fully describes multiple worked examples from the literature and beyond, allowing empirical researchers and data scientists to quickly access the 'state of the art' versioned for their domain environment, saving them time and money Disciplined structure provides latitude for multiple sources of expertise while retaining an integrated and pedagogically focused authorial voice, ensuring smooth transition and easy progression for readers Fully supported by companion site code repository 40+ diagrams of 'networks in the wild' help visually summarize key points

Author : Matthew O. Jackson
Publisher : Princeton University Press
Page : 519 pages
File Size : 42,73 MB
Release : 2010-11-01
Category : Business & Economics
ISBN : 140083399X

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Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. The many aspects of our lives that are governed by social networks make it critical to understand how they impact behavior, which network structures are likely to emerge in a society, and why we organize ourselves as we do. In Social and Economic Networks, Matthew Jackson offers a comprehensive introduction to social and economic networks, drawing on the latest findings in economics, sociology, computer science, physics, and mathematics. He provides empirical background on networks and the regularities that they exhibit, and discusses random graph-based models and strategic models of network formation. He helps readers to understand behavior in networked societies, with a detailed analysis of learning and diffusion in networks, decision making by individuals who are influenced by their social neighbors, game theory and markets on networks, and a host of related subjects. Jackson also describes the varied statistical and modeling techniques used to analyze social networks. Each chapter includes exercises to aid students in their analysis of how networks function. This book is an indispensable resource for students and researchers in economics, mathematics, physics, sociology, and business.

Author : Samuel David Johnson
Publisher :
Page : pages
File Size : 43,31 MB
Release : 2016
Category :
ISBN : 9781339825281

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As our understanding of complex social, economic, and technological systems improves, it is increasingly apparent that a full account of a system's macroscopic level properties requires us to carefully explore the structure of local, pairwise interactions that take place at the microscopic level. Over the past two decades, networks have emerged as the de facto representation of such systems, leading to the genesis of the interdisciplinary field of network science. During this same period, we have witnessed an explosion of participation and consumption of social media, advertising, and e-commerce on the internet; an ecosystem that is the embodiment of and whose success is fundamentally coupled to the use and exploitation of complex networks. What are the processes and mechanisms responsible for shaping these networks? Do these processes posses any inherent fairness? How can these structures be exploited for the benefit of strategic actors? In this dissertation, I explore these questions and present analytical results couched in a theory of strategic decision making -- algorithmic game theory. First, research is presented on the pairwise inequality that is inherent to strategic models of network formation. The network formation games that we consider model the creation of communication links between rational, self-interested individuals. We use the inequality ratio, defined as the ratio between the highest and lowest costs incurred by individual players in a given outcome, to quantify pairwise inequality. Tight upper bounds for the inequality ratio are derived for pure Nash equilibrium outcomes of the network formation games, and the relationship between inequality and efficiency (outcomes that are globally optimal) is characterized. Next, a multi-level network formation game modeled on the sociological principle of networked social capital is introduced and analyzed. Motivated by the observation that networks found in nature are rarely isolated from one another, this research examines a scenario in which individuals form intra-group links to maximize group cohesion and inter-group links to maximize their group's standing relative to other groups. Our model formulation draws heavily from the empirical research of sociologist Ronald S. Burt and his theory of structural holes, and we derive constructive proofs of the existence of equilibrium outcomes. Departing from the topic of network formation games, I next present research on the strategic seeding of opinions in social networks. This work, which is best introduced in terms of a political election, involves candidates (players) each choosing subsets of voters (nodes in a social network) to seed opinions that are subsequently spread through the voters' social connections by a dynamic process. After the opinions have been allowed to diffuse for a predetermined amount of time, the voters' opinions are aggregated in an election. Voters cast their votes probabilistically, where the probability that they choose a particular candidate is proportional to that voter's opinion toward the candidate relative to their opinion toward the other candidates. Players -- each representing a single candidate -- strategically choose a set of seed nodes that will maximize the probability that their candidate will win the election. We establish the guaranteed existence of pure Nash equilibrium outcomes in the special case where the opinion dynamics are allowed sufficient time to converge to a consensus opinion. We prove that this guarantee does not carry over to cases where the dynamics are not given sufficient time to reach a consensus. We also derive bounds on the budget multiplier, which characterizes the extent that any initial inequality (in terms of players' respective seed budgets) is amplified by the opinion dynamic over the social network into greater inequality in players' utilities. Finally, we analyze the computational problem of finding a player's best response (pure) strategy, proving that it is NP-complete but approximable to within a (1 - 1/e) factor of optimal by a simple greedy algorithm. The concluding chapter of this dissertation presents my work on algorithm instance games, which are a class of games that I have identified as being characterized by having outcomes that are derived from strategy profiles algorithmically. Primarily a conceptual contribution, this research identifies a class of games that includes algorithmic mechanism design as a special case. Two variants of a simple game from this class that is based on the Set Cover optimization problem are presented and analyzed to demonstrate how algorithmic design decisions can influence strategic behavior.

Author : Eitan Altman
Publisher : Springer Nature
Page : 322 pages
File Size : 11,65 MB
Release : 2019-10-18
Category : Mathematics
ISBN : 3030244555

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This book provides a state-of-the-art overview on the dynamics and coevolution in multi-level strategic interaction games. As such it summarizes the results of the European CONGAS project, which developed new mathematical models and tools for the analysis, prediction and control of dynamical processes in systems possessing a rich multi-level structure and a web of interwoven interactions among elements with autonomous decision-making capabilities. The framework is built around game theoretical concepts, in particular evolutionary and multi-resolution games, and includes also techniques drawn from graph theory, statistical mechanics, control and optimization theory. Specific attention is devoted to systems that are prone to intermittency and catastrophic events due to the effect of collective dynamics.