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Due to limited battery life of sensors and harsh deployment environments where they are deployed, Wireless Sensor Networks (WSNs) can be subjected to node failures. This can split the network into partitions containing healthy but unreachable nodes by the rest of the network including the sink node. One possible solution to this problem is deploying relay nodes assuming that the damaged area, the number of partitions and the location of the partitions are known to a centralized party. However, depending on the application, some of this information may not always be available, requiring a distributed self-deployment placement strategy. Such a strategy should not only guarantee the network connectivity but also strive to minimize the movement overhead on the relay nodes assuming that they are also battery-operated. In this paper, we present a distributed relay node positioning approach to address the problem of connectivity restoration in partitioned WSNs. The approach exploits Game Theory among the relay nodes and the partitions. Relay nodes determine the partitions to connect based on the probability distribution function (pdf) of the partitions. If the partition has a higher pdf, it is recovered earlier and becomes the part of the connected network. The recovery process takes place until reaching the system-wide unique Nash equilibrium. Game Theoretic approach has been shown to outperform baseline approaches under all conditions.