  This paper analyzes the behavior of selfish transmitters under imperfect
location information. The scenario considered is that of a wireless network
consisting of selfish nodes that are randomly distributed over the network
domain according to a known probability distribution, and that are interested
in communicating with a common sink node using common radio resources. In this
scenario, the wireless nodes do not know the exact locations of their
competitors but rather have belief distributions about these locations.
Firstly, properties of the packet success probability curve as a function of
the node-sink separation are obtained for such networks. Secondly, a
monotonicity property for the best-response strategies of selfish nodes is
identified. That is, for any given strategies of competitors of a node, there
exists a critical node-sink separation for this node such that its
best-response is to transmit when its distance to the sink node is smaller than
this critical threshold, and to back off otherwise. Finally, necessary and
sufficient conditions for a given strategy profile to be a Nash equilibrium are
provided.
