This paper presents a price-searching model in which a source node (Alice) seeks friendly jammers that prevent eavesdroppers (Eves) from snooping legitimate communications by generating interference or noise. Unlike existing models, the distributed jammers also have data to send to their respective destinations and are allowed to access Alice's channel if it can transmit sufficient jamming power, which is referred to as collaborative jamming in this paper. For the power used to deliver its own signal, the jammer should pay Alice. The price of the jammers' signal power is set by Alice and provides a tradeoff between the signal and the jamming power. This paper presents, in closed-form, an optimal price that maximizes Alice's benefit and the corresponding optimal power allocation from a jammers' perspective by assuming that the network-wide channel knowledge is shared by Alice and jammers. For a multiple-jammer scenario where Alice hardly has the channel knowledge, this paper provides a distributed and interactive price-searching procedure that geometrically converges to an optimal price and shows that Alice by a greedy selection policy achieves certain diversity gain, which increases log-linearly as the number of (potential) jammers grows. Various numerical examples are presented to illustrate the behavior of the proposed model.
Keywords: Stackelberg game; distributed pricing; optimal pricing; power allocation; secure capacity.