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

Tragedy of the Regulatory Commons: LightSquared and the Missing Spectrum Rights

The endemic underuse of radio spectrum constitutes a tragedy of the regulatory commons. Like other common interest tragedies, the outcome results from a legal or market structure that prevents economic actors from executing socially efficient bargains. In wireless markets, innovative applications often provoke claims by incumbent radio users that the new traffic will interfere with existing services. Sometimes these concerns are mitigated via market transactions, a la “Coasian bargaining.” Other times, however, solutions cannot be found even when social gains dominate the cost of spillovers. In the recent “LightSquared debacle,” such spectrum allocation failure played out. GPS interests that access frequencies adjacent to the band hosting LightSquared’s new nationwide mobile network complained that the wireless entrant would harm the operation of locational devices. Based on these complaints, regulators then killed LightSquared’s planned 4G network. Conservative estimates placed the prospective 4G consumer gains at least an order of magnitude above GPS losses. “Win win” bargains were theoretically available, fixing GPS vulnerabilities while welcoming the highly valuable wireless innovation. Yet transaction costs—largely caused by policy choices to issue limited and highly fragmented spectrum usage rights (here in the GPS band)—proved prohibitive. This episode provides a template for understanding market and non-market failure in radio spectrum allocation

Power Processes in Bargaining

This is a theoretical article that integrates and extends a particular program of work on power in bargaining relationships. Power is conceptualized as a structurally based capability, and power use as tactical action falling within either conciliatory or hostile categories. The core propositions are (1) the greater the total amount of power in a relationship, the greater the use of conciliatory tactics and the lower the use of hostile tactics; and (2) an unequal power relationship fosters more use of hostile tactics and less use of conciliatory tactics than an equal power relationship. Distinct research on power dependence and bilateral deterrence provides support for both propositions. Implications are discussed for power struggle in ongoing relationships

Managing in conflict: How actors distribute conflict in an industrial network

IMP researchers have examined conflict as a threat to established business relationships and commercial exchanges, drawing on theories and concepts developed in organization studies. We examine cases of conflict in relationships from the oil and gas industry's service sector, focusing on conflicts of interest and resources, and conflict as experienced by actors. Through a comparative case study design, we propose an explanation of how actors manage conflict and manage in conflict given that they tend to value and maintain relationships beyond episodes of exchange. We consider conflicts in relationships from a network perspective, showing that actors experienced these while adapting to changes in their business setting, modifying their roles in that network. By identifying conflict with the organizing forms of relationship and network, we show how actors formulate conflict through pursuing and combining a number of strategies, distributing the conflict across an enlarged network

Bartering integer commodities with exogenous prices

The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This research report provides a mathematical and computational details associated to the mathematical programming based approaches proposed by Nasini et al. (accepted 2014) to study pure exchange economies where discrete amounts of commodities are exchanged at fixed prices. Barter processes, consisting in sequences of elementary reallocations of couple of commodities among couples of agents, are formalized as local searches converging to equilibrium allocations. A direct application of the analyzed processes in the context of computational economics is provided, along with a Java implementation of the approaches described in this research report.Comment: 30 pages, 5 sections, 10 figures, 3 table

Joint Head Selection and Airtime Allocation for Data Dissemination in Mobile Social Networks

Mobile social networks (MSNs) enable people with similar interests to interact without Internet access. By forming a temporary group, users can disseminate their data to other interested users in proximity with short-range communication technologies. However, due to user mobility, airtime available for users in the same group to disseminate data is limited. In addition, for practical consideration, a star network topology among users in the group is expected. For the former, unfair airtime allocation among the users will undermine their willingness to participate in MSNs. For the latter, a group head is required to connect other users. These two problems have to be properly addressed to enable real implementation and adoption of MSNs. To this aim, we propose a Nash bargaining-based joint head selection and airtime allocation scheme for data dissemination within the group. Specifically, the bargaining game of joint head selection and airtime allocation is first formulated. Then, Nash bargaining solution (NBS) based optimization problems are proposed for a homogeneous case and a more general heterogeneous case. For both cases, the existence of solution to the optimization problem is proved, which guarantees Pareto optimality and proportional fairness. Next, an algorithm, allowing distributed implementation, for join head selection and airtime allocation is introduced. Finally, numerical results are presented to evaluate the performance, validate intuitions and derive insights of the proposed scheme

Matching structure and bargaining outcomes in buyer–seller networks

We examine the relationship between the matching structure of a bipartite (buyer-seller) network and the (expected) shares of the unit surplus that each connected pair in this network can create. We show that in different bargaining environments, these shares are closely related to the Gallai-Edmonds Structure Theorem. This theorem characterizes the structure of maximum matchings in an undirected graph. We show that the relationship between the (expected) shares and the tructure Theorem is not an artefact of a particular bargaining mechanism or trade centralization. However, this relationship does not necessarily generalize to non-bipartite networks or to networks with heterogeneous link values