An FPTAS for Bargaining Networks with Unequal Bargaining Powers

Bargaining networks model social or economic situations in which agents seek to form the most lucrative partnership with another agent from among several alternatives. There has been a flurry of recent research studying Nash bargaining solutions (also called 'balanced outcomes') in bargaining networks, so that we now know when such solutions exist, and also that they can be computed efficiently, even by market agents behaving in a natural manner. In this work we study a generalization of Nash bargaining, that models the possibility of unequal 'bargaining powers'. This generalization was introduced in [KB+10], where it was shown that the corresponding 'unequal division' (UD) solutions exist if and only if Nash bargaining solutions exist, and also that a certain local dynamics converges to UD solutions when they exist. However, the bound on convergence time obtained for that dynamics was exponential in network size for the unequal division case. This bound is tight, in the sense that there exists instances on which the dynamics of [KB+10] converges only after exponential time. Other approaches, such as the one of Kleinberg and Tardos, do not generalize to the unsymmetrical case. Thus, the question of computational tractability of UD solutions has remained open. In this paper, we provide an FPTAS for the computation of UD solutions, when such solutions exist. On a graph G=(V,E) with weights (i.e. pairwise profit opportunities) uniformly bounded above by 1, our FPTAS finds an \eps-UD solution in time poly(|V|,1/\eps). We also provide a fast local algorithm for finding \eps-UD solution, providing further justification that a market can find such a solution.Comment: 18 pages; Amin Saberi (Ed.): Internet and Network Economics - 6th International Workshop, WINE 2010, Stanford, CA, USA, December 13-17, 2010. Proceedings

A theory on power in networks

The eigenvector centrality equation $\lambda x = A \, x$ is a successful compromise between simplicity and expressivity. It claims that central actors are those connected with central others. For at least 70 years, this equation has been explored in disparate contexts, including econometrics, sociometry, bibliometrics, Web information retrieval, and network science. We propose an equally elegant counterpart: the power equation $x = A x^{\div}$, where $x^{\div}$ is the vector whose entries are the reciprocal of those of $x$. It asserts that power is in the hands of those connected with powerless others. It is meaningful, for instance, in bargaining situations, where it is advantageous to be connected to those who have few options. We tell the parallel, mostly unexplored story of this intriguing equation

Reconsidering Cohesion Policy : the Contested debate on Territorial Cohesion

The incorporation of territorial cohesion as a regional policy objective has focused attention on the potential role of territorial cooperation in pursuing this goal. However, the broad agreement on the positive effects of territorial cooperation is not always matched by the same enthusiasm when funds are being allocated. The concrete impact of territorial cooperation is often difficult to identify. At the same time, in terms of the qualitative impacts of territorial cooperation, the added value of INTERREG for territorial cohesion is difficult to dispute

Spatial interactions in agent-based modeling

Agent Based Modeling (ABM) has become a widespread approach to model complex interactions. In this chapter after briefly summarizing some features of ABM the different approaches in modeling spatial interactions are discussed. It is stressed that agents can interact either indirectly through a shared environment and/or directly with each other. In such an approach, higher-order variables such as commodity prices, population dynamics or even institutions, are not exogenously specified but instead are seen as the results of interactions. It is highlighted in the chapter that the understanding of patterns emerging from such spatial interaction between agents is a key problem as much as their description through analytical or simulation means. The chapter reviews different approaches for modeling agents' behavior, taking into account either explicit spatial (lattice based) structures or networks. Some emphasis is placed on recent ABM as applied to the description of the dynamics of the geographical distribution of economic activities, - out of equilibrium. The Eurace@Unibi Model, an agent-based macroeconomic model with spatial structure, is used to illustrate the potential of such an approach for spatial policy analysis.Comment: 26 pages, 5 figures, 105 references; a chapter prepared for the book "Complexity and Geographical Economics - Topics and Tools", P. Commendatore, S.S. Kayam and I. Kubin, Eds. (Springer, in press, 2014