Accountability in Dynamic Networks

Abstract

A variety of distributed protocols require pairs of neighbouring nodes of a network to repeatedly interact in pairwise exchanges of messages of mutual interest. Well known examples include filesharing systems [4] and gossip dissemination protocols [18,17], among many other examples. These protocols can operate in very diverse settings such as wireless ad-hoc or peer-to-peer overlay networks. These settings pose three main challenges. First, networks are inherently dynamic, whether due to uncontrolled mobility or maintenance of the overlay. Second, since communication may be costly, nodes may act rationally by not sending messages, while still receiving messages from their neighbours. Third, nodes may have incomplete information about the network topology. In this work, we aim at gaining theoretical insight into how to persuade agents to exchange messages in dynamic networks.We take a game theoretical approach to determine necessary and sufficient conditions under which we can persuade rational agents to exchange messages, by holding them accountable for deviations with punishments. Unlike previous work [19,6,7,5,20,18,17,9], we do not assume the network is the result of rational behaviour or that the topology changes according to some known probability distribution, and we do not limit our analysis to one-shot pairwise interactions. We make three contributions: (1) we provide a new game theoretical model of repeated interactions in dynamic networks, where agents have incomplete information of the topology, (2) we define a new solution concept for this model, and (3) we identify necessary and sufficient conditions for enforcing accountability, i.e., for persuading agents to exchange messages in the aforementioned model.Our results are of technical interest but also of practical relevance. We show that we cannot enforce accountability if the dynamic network does not allow for timely punishments. In practice, this means for instance that we cannot enforce accountability in some networks formed in file-sharing applications such as Bittorrent [4]. We also show that for applications such as secret exchange, where the benefits of the exchanges significantly surpass the communication costs, timely punishments are enough to enforce accountability. However, we cannot in general enforce accountability if agents do not possess enough information about the network topology. Nevertheless, we can enforce accountability in a wide variety of networks that satisfy 1-connectivity [15] with minimal knowledge about the network topology. This result provides a sound game theoretical foundation for the empirical results presented in [18,17,9], showing that we can in fact enforce accountability in gossip dissemination with connected overlay networks where nodes possess sufficient information about the network. * 1 Henceforth, we use the designation agent when referring to both the node and the rational agents.