Perhaps, you can indicate which article or statement of Mearsheimer you refer to.  I thought you referring to these articles but I am uncertain now.

http://www.foreignaffairs.com/articles/141769/john-j-mearsheimer/why-the-ukraine-crisis-is-the-wests-fault

http://mearsheimer.uchicago.edu/pdfs/A0021.pdf

I have looked at the article by Beyer (2014) you have noted above. She is not apparently making a liberal and realist distinction, unless you equate "liberal" with "defensive realism" and "offensive realism' with being a realist.

Beyer wrote or posits: 

(1) States pursue absolute gains first, then relative gains.

What Beyer distinguishes is helpful in focusing on control as equating the power that states strive toward or are motivated by.  However, her Posit 2 below is embedded in this frame and raises a lot of questions about her assumptions

Beyer wrote or posits:

(2) Relative gains are pursued in response to threats, not generally.

Due to the role of media and pressure groups, I do not feel that relative gains are always second to absolute gains.  Perceptions are important.  Constructivists do a much better job than realists in explaining the role of such groups in policy and practices, but in a nutshell sometimes absolute gains are important and at other times nations or regime leadership focus only on hegemonic gains or balancing.

Beyer wrote or posits:

(3) Acquiring latent power requires states to cooperate, making cooperation inherently necessary, even for defensive realists.

I agree with this but it is all subservient internal pressure groups and worldviews that come to dominate either in the media, thinktanks, lobbies, or other powerful corners of society. 

Beyer wrote or posits:

(4) Balancing does take place, and not only between major powers, but also at other levels of analysis, and in other areas of international affairs.

Her usage of balancing here is in a way extremely similar to that used by hegemonic theorists.  Both Neo-conservatives and Neo-realists by into hegemonic theories at times.

Beyer wrote or posits: 

(5) Balancing will be mitigated by good relations. When relations are good, balancing does not need to occur.

Balancing can mean also that balancing is acceptable because other things are more important than competing.

In summary, whether we are referring to Beyer or to offensive realism, proposed by John Mearsheimer, all these frameworks: hegemonic theory or various forms of realism or constructivism all are applicable to the Middle East where I live or to the USA where I am from--or to East Asia where I travel often. 

Regarding what you have mentioned about possible application of all theories on the Middle East situation, the current situation of Iraq and Syria proves the fragility of regional cooperation over security issues between regional players of Middle East.  Even between Arab countries in Arab League there is no united front to combat extri ism. The other example of that is case of Syria and its representation in  the League which is the matter of disagreement between member states. The absolute gain notion which bears cooperation can be applied on 

the European model of cooperation on some part of the world. But first of all it should be considered whether the nation state process in member states of a regional security complex has been concluded and resulted to establishment of a democratic structure. The democratic structure which allows rotation of power between different political factions and prepares them for broader cooperation on regional spectrum. In reality the case of Middle East is the reflection of states efforts for survival and fragility of integration between different sect within states and second the desire of active players for superiority which due to internal division and foreign powers meddling is more and more increasing. Therefore the notion of cooperation with absolute gain versus relative gain which is accompanied with conflict is more prevailed and proves the viability of Mearsheimer's argument on importance of superiority within a regional security architecture like the Middle East with instability and lack of consensus regarding buffer and power zones. 

Amir, are you fully cognizant (in your arguments here) of how hegemonic theory was developed by realists or conservatives?  They do not require any liberal government to be involved in the process.  In contrast neo-liberal and liberal ones do.  

It appears you are arguing against a liberal application but you are not taking on the hegemonic theories and evaluations of realists or conservatives and neo-cons.

ftp://cpsa-acsp.ca/cpsa-acsp/papers-2005/Nuruzzaman.pdf

I don't buy into  half of what they say, but the other half of what they are arguing is worth considering.  They, too, need to be brought into discussion with the neo-liberal ones.  

Cognitivists need to be added too. 

http://wsetiabudi.files.wordpress.com/2008/12/critiques-of-the-theory-of-international-regimes1.doc

Dear Kevin 

My main theme is application of relative gains based on Dr Beyer's argument over importance of absolute gains over relative gains in international politics. In general we all praise the vitality of cooperation in international politics and its capability to bring peace and security among community of states. But in reality Mearsheimer's argument shows importance of superiority in some parts of the world due to some challenges among and within the states. The hypothesis which Cornelia used to describe the cooperation between states is its function and it occurred among European countries specially a concert of former European powerful states which at the moment are also effective in EU. If we want to apply the viability of relative gains we can refer it the the Middle East. My main interest in elaboration of offensive realists like Mearsheimer is the effort to concentrate over the nature of power and its effect on states behaviors in different regional security complexes around the world to prove the fragility of Cornelia's argument on importance of absolute gains in current international politics. 

Thanks,  Amir.

Who is however best able to objectively and subjectively determine which variables make up absolute gains and which gains are only relative?

Doesn't this depend on where someone is standing or what values one has to begin with (or at the end of one's thought or research experiment)?

Dear Kevin 

This is something which I wanted to point out. The theories of international relations are general frameworks which allow us to think harmonically and connect varied phenomenons to get the meanings from them. Those theories empower us to establish meaningful analysis from actual facts and figures.

But the problem which I think is our's source of discussion is the way in which we develop our meaning and try to expand it to other parts of the world.

I mean that the emergence of new theories and frameworks of analysis which now a days are heavily discussed (and mostly called non western theories of International relations) try to reshape the concepts of power and cooperation and conflict in light of their interest and perspectives.

So it depends to the geographical or development aspect of country or group of countries, but please bear in your mind that even between developed and western countries the concept of relative gains and absolute gains is matter of discussion.

I can refer you to two examples: First the Iraq invasion which between U.S. and its European allies there were a matter of great discussion on legitimacy of invasion without UNSC mandate. 

Second, even in EU there is matter of discussion over power and representation of smaller EU states and their right in light of power projection of powerful states like France and Germany and constant dissatisfaction of Conservative party of UK and its threat to withdrawn form EU. 

I think that despite differences regarding geography and the level of development the case of relative gain versus absolute gain is always matter of discussion and analysis and it continues it vitality in international politics which is matter of power and interest.