Government Response
The Nigerian government has yet to choose a definite strategy to deal with the group. They claimed to have killed a total of 31 members although the group denies 20 of these casualties. Nigeria's government is known for its counter-productive extra-judicial executions which in the case of Boko Haram, has fueled more hate against the government. Minister of Information Labaram Maku has stated "The Federal Government welcomes any initiative that will usher in peace, security and tranquility in the country, especially in the light of the security challenges that we have faced in the last two years." In fact, one initiative was to trace and block the groups financial support. The government detected private funding by its members, donations by Al-Qaeda in the Islamic Maghreb and Islamist donors from the U.K, though the investigations have accounted only for a small portion of their funding.
In March 2012, an alleged spokesman for Boko Haram contacted BBC and the federal government to begin negotiations but the core of the group denied interest and is believed to have killed the spokesman following their habit of beheading members who they believe do not properly represent the sect.
IR Theories Applied
The fact that Boko Haram has not made any international attacks or connections with the governments of sovereign states, and Nigeria's openness to different approaches make it hard to pin-point which IR theory is mostly applied when dealing with the terrorist group.
Realism stresses the concept of power of men over men and relative gains. In this case, the Nigerian government has used armed forces to conduct executions to gain the upper hand against the group at times but has failed to fully eliminate the threat (did so much as to only have a relative advantage). Realism however cannot be applied to its full extent because to realists, there is no actor above the states, so the states harboring terrorism must be pressured to stop it. Boko Haram's monetary connections in Algeria and the United Kingdom are not with the official governments. One could, however, suggest that the Nigerian government begin talks with the governments of these countries to weaken and ultimately obliterate Boko Haram's connections.
Liberalism's final goals are to unify the world economically and set representative democracy as a standard. Terrorist groups are seldom fighting for any of this. Liberalism does however stress the importance of non-state actors and international conventions to deal with them. The Nigerian police has little interest in this, since requesting an international institution such as Humans Rights Watch would most likely put an end to their current practices which include holding family members of terrorists as hostages and extracting bribes and road-blocks intended to intercept arms.
In conclusion, the theory applied in this case is realism, since it provides grey areas for the Nigerian government to act freely. The best solution for the problem would be a combination of both since they do not necessarily oppose each other in this case, The Nigerian government could very well abide by international conventions while contacting the governments of the countries where their supporters reside.