What's the dual problem of stable matching?
From http://kuznets.fas.harvard.edu/~aroth/papers/1993_MOR_StableMatchingsOptimal.pdf :


  Shapley and Shubik (1972) observed that [the dual] formulates the problem of finding payoff vectors in the core of the above assignment game.


The assignment game described is that two agents who choose to match get a total "value" equal to the edge weight between them, and they can split this value between them in some way; these are the "payoffs".

It might be nice for future readers if you put the LP and dual in your question....