Equilibria in Topology Control Games for Ad Hoc Networks

We study topology control problems in ad hoc networks where network nodes get to choose their power levels in order to ensure desired connectivity properties. Unlike most other work on this topic, we assume that the network nodes are owned by different entities, whose only goal is to maximize their own utility that they get out of the network without considering the overall performance of the network. Game theory is the appropriate tool to study such selfish nodes: we define several topology control games in which the nodes need to choose power levels in order to connect to other nodes in the network to reach their communication partners while at the same time minimizing their costs. We study Nash equilibria and show that—among the games we define—these can only be guaranteed to exist if each network node is required to be connected to all other nodes (we call this the Strong Connectivity Game). For a variation called Connectivity Game, where each node is only required to be connected (possibly via intermediate nodes) to a given set of nodes, we show that Nash equilibria do not necessarily exist. We further study how to find Nash equilibria with incentive-compatible algorithms and compare the cost of Nash equilibria to the cost of a social optimum, which is a radius assignment that minimizes the total cost in a network where nodes cooperate. We also study variations of the games; one where nodes not only have to be connected, but k-connected, and one that we call the Reachability Game, where nodes have to reach as many other nodes as possible, while keeping costs low. We extend our study of the Strong Connectivity Game and the Connectivity Game to wireless networks with directional antennas and wireline networks, where nodes need to choose neighbors to which they will pay a link. Our work is a first step towards game-theoretic analyses of topology control in wireless and wireline networks. A preliminary version of this paper appeared in DIALM-POMC ’03 8]. Stephan Eidenbenz is a technical staff member in Discrete Simulation Sciences (CCS-5) at Los Alamos National Laboraotry. He received his Ph.D. in Computer Science from the Swiss Federal Institute of Technology, Zurich, Switzerland in 2000. Stephan’s research covers areas in approximability, algorithms, computational geometry, computational biology, large-scale discrete simulation, selfish networking, efficient networking, protocol design and optimization. V. S. Anil Kumar is currently an Assistant Professor in the Dept. of Computer Science and a Senior Research Associate at Virginia Bioinformatics Institute, Virginia Tech. Prior to this, he was a technical staff member in Los Alamos National Laboratory. He received a Ph.D. in Computer Science from the Indian Institute of Science in 1999. His research interests include approximation algorithms, mobile computing, combinatorial optimization and simulation of large socio-technical systems. Sibylle Zust received her Masters degree in mathematics from ETH Zurich in Switzerland in 2002. She wrote her diploma thesis at the University of Copenhagen in Denmark. Sibylle Zust spent two and a half years (2002–2005) as a graduate research assistant at the Los Alamos National Laboratory in New Mexico, USA, where she worked on algorithmic aspects of game theory and scheduling problems. She now works for an insurance company in Zurich, Switzerland.