Convergence of Local Dynamics to Balanced Outcomes in Exchange Networks

Abstract

Bargaining games on exchange networks have been studied by both economists and sociologists. A Balanced Outcome [10,16] for such a game is an equilibrium concept that combines notions of stability and fairness. In a recent paper, Kleinberg and Tardos [14] introduced balanced outcomes to the computer science community and provided a polynomial-time algorithm to compute the set of such outcomes. Their work left open a pertinent question: are there natural, local dynamics that converge quickly to a balanced outcome? In this paper, we provide a partial answer to this question by showing that simple edge-balancing dynamics converge to a balanced outcome whenever one exists. * azar@tau.ac.il,

A behavioral study of bargaining in social networks

“…The model given by Cook and Yamagishi, sometimes referred to as equidependence theory, is the most recognized theoretical model, and has received a lot of recent focus from the theoretical computer science community [13,1]. Though Cook and Yamagishi [8] considered only unique exchange networks (that is, where each vertex may close only a single deal), the model is easily extendable to networks with varying deal limits.…”

“…We were partly inspired by a long line of previous theoretical work which tried to relate wealth to network topology in bargaining settings [8,9,2,14,4,13,1,5]. A notable feature of these theories is the prediction that there may be significant local variation in splits purely as a result of the imposed deal limits and structural asymmetries in the network.…”

Optimizing Social Welfare for Network Bargaining Games in the Face of Unstability, Greed and Spite

“…Bargaining games have been studied with a long history, early in economics [19] and sociology, and recently in computer science, there has been a lot of attention on bargaining games in social exchange networks [16,1,4,15], in which users are modeled as nodes in an undirected graph G = (V, E), whose edges are weighted. An edge {i, j} ∈ E with weight w ij > 0 means that users i and j can potentially form a contract with each other and split a profit of w ij .…”

“…al [1] considered a local dynamics that converges to a balanced outcome provided that it exists. Assuming that the LP relaxation for matching has a unique integral optimum, Kanoria et.…”

“…Formally, each edge {i, j} has the action set A ij := {(x, y) : x ≥ 0, y ≥ 0, x+y ≤ w e }, where a proposal (x, y) means that node i gets amount x and j gets amount y. 1 Based on the configuration m ∈ A E := × e∈E A e of proposals made by all the agents, a selection process (which can be randomized) will choose a b-matching M , which is the set of contracts formed. An agent e will receive a commission if his proposal is selected; his payoff u e (m) is the probability that edge e is in the matching M returned.…”