Jay Cost has an excellent post up gaming out the Obamacare stalemate from the perspective of the relevant players in this high stakes political game:

-Stupak’s Pro-Lifers
-Senate Republicans
-Senate Democrats

Recall, we discussed game theory using the strategic or normal form to describe some basic games to use in understanding politics. Cost uses a game tree or the “extensive form” to describe the game theoretic problem that Brown’s victory in MA presents to Democrats wanting to pass health care. In particular the problem for Stupak, a pro-life Democrat who wants language forbiding federal money for abortions in the reconcilliation package sent to the Senate.

On the one hand, the Republicans are threatening to object to the Stupak language in a reconcilliation package. This would mean that the health care bill wouldn’t specifically forbid funding for abortion, a deal-breaker for the Democratic Pro-Lifers in the House. But, as Cost notes, this is a “non-credible threat.” In game theory, a non-credible threat is a course of action (Y) that a player (A) could take if the other player (B) chooses X, but where it simply isn’t believable that player A would actually choose Y, since it leads to a lower payoff for player A. Player A “threatens” to choose Y to try and forestall player B’s choice of X. But since it isn’t credible, player B should ignore it.

In this case, we can use backwards induction to solve for the subgame perfect equilibrium that reveals the noncredible threat.

As Cost notes, if the Republicans are raising a point of order about the Stupak language, then this means the Senate Bill has already passed. So they are left with the choice of having Obamacare with Stupak or without. Since they perfer the Stupak language to nothing, their point of order objection is a non-credible threat. Solving the game yields an equilibrium where the House passes Obamacare, and the Republicans vote for Stupak’s langage.

But not so fast! It is Democrats who enjoy the majority in the Senate. And working from reconcilliation, they only need to raise that same point of order to force a 60 vote supermajority necessary to pass the Stupak language. As Cost argues, any guarantee by the Senate Democrats to include Stupak’s abortion language is an “empty promise.” Why? For the *same* reason. The Senate bill will have already passed. What incentive then do the Senate Democrats have to adopt language they have already rejected?

Answer: none.

Stupak has a problem. Essentially he is left with the following best case scenarios (ignoring the possibility that he can’t even get Stupak language into the House reconcilliation bill or that his block is irrelevant to passage):

- get the House to include his abortion language, vote for the bill, and see that language stripped in the reconilliation process–by the Democrats, not the Republicans–when it is taken up by the Senate post-passage of Obamacare.

- vote against Obamacare in the House, thus defeating the Democratic effort at health care reform.

Neither choice is particularly palatable to a principled Pro-Life Democrat who wants to remain a Democrat after this vote. But if we believe his “cheap talk” that he would rather have no bill than a bill that permits some form of federal abortion funding, then his sub-game perfect optimal choice would be to vote against the bill. If, however, that “cheap talk” is just a gambit to get his amendment passed…and, in fact, he would prefer Obamacare w/ federal funding of abortions to no bill at all…then we should expect Stupak to cave.

Cost raises the only possible solution outside of those two choices: get the Senate Democrats to act first.

I think the only solution for Stupak is somehow to find a way for the Senate to act first on abortion. This is the most important point: when Stupak and his bloc cast their votes in the House, their leverage is completely gone. That’s the only power they have in the process. If they are induced to go first, they will lose to the Senate liberals.

This may be why the “Slaughter Solution” has begun to get some traction this week. The Slaughter solution (where passage of the reconcilliation bill will be ‘deemed’ by the House to have been a simulataneous passage of the original Senate Obamacare bill) is an effort to avoid the dilemma of sequential moves that Cost describes above. If the Senate bill isn’t ‘passed’ until the Senate approves the House reconcilliation package, then Stupak doesn’t ‘lose’ his leverage. Then again, if it is deemed to have ‘passed’ with the vote on reconcilliation…that seems to be exactly what does happen: the Senate bill passes. Which puts us right back in the same spot (plus a potential constitutional issue). Maybe Slaughter is just about tricking dumb House Democrats into believing that this will get their reconcilliation language adopted by the Senate in toto…despite the fact they have no incentive to do it.

Constitutional issues aside, this seems a rather large hurdle for Obamacare: without a procedure that either inverts or eliminates the current sequence, there is no way to pass a reconcilliation bill with Stupak langage that the Senate would retain.