If one wanted to apply game theory to national politics, as a first pass one could roughly model it as a "board" with N "issues", each issue has 3 positions: conservative, moderate, progressive. Each position has a payoff that is a function of the opponents choices, the rest of the board, what we seem to call "branding", and the "focus" the candidate draws to that issue. Candidates have limited "focus" to spend, and how they spend it determines the election.
On immigration, for example, the conservative position is deport all illegals, the moderate position is to grant illegal immigrants extended, or permanent residency, and a "back-of-the-line" path to citizenship, but stop future illegal immigration, the progressive position would grant illegal immigrants a path to citizenship and do nothing effective to stop future illegal immigration. Romney's position "self-deportation" was understood by the electorate as, effectively, the conservative one, which was helpful in the primaries. In the general, taking the moderate position would not have cost Romney many conservative voters -- who had higher priorities -- and would have forced Obama to clarify better where he stood -- forcing him to alienate some of his own voters. While there is good reason to believe the direct payoff would have been small, there would have been indirect "branding" payoff had Obama, or other Democrats, been cornered into clearly taking the progressive position.
On abortion, Democratic politicians mostly believe abortion should be always and everywhere legal, most voters believe it should be sometimes, or in some places (=federalism) legal and many conservative Christian voters believe it should be always and everywhere illegal. The Obama campaign spent a great deal of its focus and was successful in making an issue of the conservative Christian position taken by two Senate candidates, severely impairing the Republican brand. Almost more than any other issue, this buried Romney.
Romney chose, instead, to spend his focus on Obama's partisan lack of leadership, his unwillingness reach across the aisle to get things done for America. This choice was undercut, fatally, by Sandy and Christie. While its impossible to prove one way or the other, from the polls and the post-election reactions of both candidates, the notion that Sandy/Christie turned the election is credible.
Finally, the results reflected that in spending focus on "branding", Obama helped downstream democrats. Romney's focus spent on Obama's personal failings (and his success, in contrast) offered no such help.