Dr. John Nash: "And the [Debt Ceiling Standoff] Winner Is..."

The Reps AND the Dems!  "Win" will be loosely defined here as "getting what you wanted."  But how?  Why?  Well, we can make quick work of a two-player, non-temporal game set (player one = Reps, player two = Dems).  Let's analyze the players' decisions given the two hot-button issues:  1) Raising/No Raising the Debt Ceiling, and 2) Hiking/Not Hiking Taxes.

If you're the Reps, your list of preferred outcomes (ordered by preference) would look like this:
1.  No Raising of the Ceiling/No Tax Hikes (Absolute win by Reps)
2.  Raising of the Ceiling/No Tax Hikes
3.  No Raising of the Ceiling/ Tax Hikes
4.  Raising of the Ceiling/Tax Hikes (Absolute loss by Reps)

If you're the Dems, your list of preferred outcomes (again, ordered by preference) would look like this:
1.  Raising the Ceiling/Tax Hikes  (Absolute win by Dems)
2.  Raising the Ceiling/No Tax Hikes
3.  No Raising of the Ceiling/Tax Hikes
4.  No Raising of the Ceiling/No Tax Hikes (Absolute loss by Dems)

Now that we have our player/preference data, we can simply wave the magic wand of Game Theory over these values and determine that the Nash equilibrium (thus, the likely outcome) will be Dems concede on taxes, and Reps concede on the debt ceiling.  Essentially, no one will really gain much at all.  The standoff will simply end with an 11th hour concession swap agreement...then it's back to some bigger/faster/stronger version of square one.  Dems won't push for higher taxes if Reps won't push for a firm debt ceiling.  This is your strategic outcome.