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 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 ). ...

• Type: Journal
• Year: 2008
• Where: JSAC
• Authors: Xin Ai, Vikram Srinivasan, Chen-Khong Tham
• Keywords: JSAC 2008, Nash Equilibria, Nash Equilibrium, Pure Nash Equilibria