President Obama is cutting his Christmas holiday short, returning to Washington for a last attempt at avoiding the fiscal cliff. But he’s running headlong into the Republican strategy of fanaticism.

It’s a long-established principle of game theory (see Thomas Schelling’s classic 1956 essay in the American Economic Review) that a fanatic who restricts his freedom to avert a disaster puts maximum pressure on his opponent to give ground.

In a game of highway chicken, for example, the driver that can’t swerve because he’s tied his hands to the steering wheel and chained his foot to the accelerator forces the other to swerve in order to avoid crashing.

The trick is for the first driver to convince the second that he’s crazy enough to have committed himself to instant death if the second doesn’t act rationally.

House Speaker John Boehner’s failure to persuade rank-and-file House Republicans to raise taxes even on millionaires fits the fanatic’s strategy exactly. Boehner can now credibly claim he has no choice in the matter – Republican fanatics in the House have tied his hands and manacled his feet — so the only way to avoid going over the cliff is for Obama and the Democrats to make more concessions.

The White House’s hope of getting the Senate to pass legislation that raises taxes on the wealthy in order to pressure Boehner won’t work because the legislation can’t possibly get through the House. That’s the point: Boehner has demonstrated he has no choice; the fanatics are in charge there.

Obama could decide going over the cliff isn’t so bad after all – as long as he and congressional Democrats introduce legislation early in the 2013 that gives a tax cut to the middle class retroactively to January 1st (extending the Bush tax cut to the first $250,000 of income) and restores most spending — andRepublicans feel compelled to go along.

But with Boehner’s hands tied and the fanatics in charge, this gambit becomes far riskier. What if we go over the cliff and House Republicans continue to hold out against any tax increases on the rich while demanding major cuts in Medicare and Social Security?

The path of least resistance is for Obama and the Democrats to offer to keep everything as is, through 2013 – extend all the Bush tax cuts and continue all current spending (lifting the debt limit along the way) – unless or until a “grand bargain” on the budget is agreed to before the end of the next year.

This is likely to satisfy enough Republican fanatics to gain a majority in the House. And it would avoid the fiscal cliff, kicking the can down the road and giving everyone more time.

Deficit hawks in both parties won’t like it, but that’s okay. Unemployment is still way too high and growth too meager to justify trimming the deficit any time soon.

The real problem with this gambit is it doesn’t change the game. Even down the road, Boehner’s hands will still be tied and the fanatics will remain in charge — which will give Republicans the stronger position in negotiations leading to a “grand bargain.” Compromise would have to be almost entirely on the Democrats’ side.

That’s why I’d recommend going over the cliff and forcing the Republicans’ hand. It’s a risky strategy but it would at least expose the Republican tactic and put public pressure squarely on rank-and-file Republicans, where it belongs.

The fanatics in the GOP have to be held accountable or they’ll continue to hold the nation hostage to their extremism. Even if it takes until the 2014 midterms to loosen their hold, the cost is worth it.

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