Optimality and Complexity of Pure Nash Equilibria in the Coverage Game

In this paper, we investigate the coverage problem in wireless sensor networks using a game theory method. We assume that nodes are randomly scattered in a sensor field and the goal is to partition these nodes into K sets. At any given time, nodes belonging to only one of these sets actively sense t...

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Bibliographic Details
Published in:IEEE journal on selected areas in communications Vol. 26; no. 7; pp. 1170 - 1182
Main Authors: Xin Ai, Srinivasan, V., Chen-khong Tham
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2008
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Computational modeling
Convergence
coverage
Game theory
Nash equilibrium
Partitioning algorithms
Scattering
Search problems
Studies
Wireless sensor networks
Working environment noise
ISSN:0733-8716, 1558-0008
Online Access:Get full text
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Summary:In this paper, we investigate the coverage problem in wireless sensor networks using a game theory method. We assume that nodes are randomly scattered in a sensor field and the goal is to partition these nodes into K sets. At any given time, nodes belonging to only one of these sets actively sense the field. A key challenge is to achieve this partition in a distributed manner with purely local information and yet provide near optimal coverage. We appropriately formulate this coverage problem as a coverage game and prove that the optimal solution is a pure Nash equilibrium. Then, we design synchronous and asynchronous algorithms, which converge to pure Nash equilibria. Moreover, we analyze the optimality and complexity of pure Nash equilibria in the coverage game. We prove that, the ratio between the optimal coverage and the worst case Nash equilibrium coverage, is upper bounded by 2 - 1/m+1 (m is the maximum number of nodes, which cover any point, in the Nash equilibrium solution s*). We prove that finding pure Nash equilibria in the general coverage game is PLS-complete, i.e. "as hard as that of finding a local optimum in any local search problem with efficient computable neighbors". Finally, via extensive simulations, we show that, the Nash equilibria coverage performance is very close to the optimal coverage and the convergence speed is sublinear. Even under the noisy environment, our algorithms can still converge to the pure Nash equilibria.
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ISSN:0733-8716
1558-0008
DOI:10.1109/JSAC.2008.080914