The Hitchhiker’s Guide to the Ole Miss Debate

John McCain will attend the debate at Ole Miss tonight.
No, he hasn’t made an announcement. But I’m fairly confident he will, and I have been since yesterday morning. How am I so confident? Game theory. Now, game theory doesn’t give you answers. But it does help you discipline your intuition, requiring you to first be explicit about your assumptions and then helping you see their interaction without allowing extraneous considerations to cloud the picture. So think of game theory (or any formal modeling) as Photoshop: it can remove the red-eye and clear up the resolution, but you still take the picture.
So let’s look at McCain’s situation. There are two players, McCain and Obama. They have two choices: attend the Mississippi debate or not. So there are four potential outcomes:

1. Both attend the debate.
2. Obama attends the debate, but McCain does not.
3. McCain attends the debate, but Obama does not.
4. Both skip the debate to attend to other (allegedly more pressing) matters.
Now, McCain would most like the fourth option. He leads, Obama follows—essentially, it highlights the theme of his campaign, that he’s a better leader. Heck, Obama would be implicitly endorsing his leadership. His next best outcome is that both attend the debate. At least, this is certainly better than Obama having the media all to himself when he attends and McCain does not. Worst of all would be McCain attending while Obama goes to DC—he gets Kerry-ed in the press, Obama looks like the leader.
Obama’s best outcome is McCain staying in Washington—he gets the media in Mississippi to himself. Both attending is second for him, too. Following McCain to DC is slightly better than following McCain only to have McCain ditch him—he looks like the younger brother tagging along behind.
So here are the options again, with their payoffs (McCain’s is listed first):
1. Both attend the debate. (3,3)
2. Obama attends the debate, but McCain does not. (2,4)
3. McCain attends the debate, but Obama does not. (1,1)
4. Both skip the debate to attend to other (allegedly more pressing) matters. (4,2)
One thing this tells us: Obama has a dominant strategy (one that performs better, regardless of the other player’s choice). If McCain attends, Obama gets 3 for attending, 1 for not. If McCain does not attend, Obama gets 4 for attending, 2 for not. He should always attend (and he quickly announced he would).
Knowing this, McCain should attend. He doesn’t have a dominant strategy, but he should know that Obama DOES. And his best response to that strategy is to attend himself (3, rather than 2). Now, he should have figured this out beforehand, but I imagine it’s becoming painfully clear to him now. It’s really the first misstep from McCain’s campaign. He’s made a “threat,” tried to convince Obama that his preferences are other than what they are. But it’s not a credible threat—Obama’s actually better off if McCain does stay in DC.
What this means is that McCain will suddenly discover either that they have made sufficient progress to allow him to nip off to keep his commitments in Mississippi, or that the decision about policy will still be prolonged into next week—also allowing him the luxury of time to debate Obama in Mississippi. (In all honesty, I worked through this yesterday morning with one of my classes—and last night, McCain was on the news explaining that they were making good progress and would continue to make good progress.)
Of course, this is a model, and it is sensitive to the assumptions we put in. McCain may be playing a different game. For example, if we consider this as one iteration (or episode) in a longer series of games, the loss here could produce a benefit in later iterations. After all, his campaign theme is “Country First,” and neglecting his interests for the benefit of his country would reinforce that message.
Still, even if that was his thinking, I’m pretty sure he realizes that it’s not reading that way—the common response seems to be that we need economists more than politicians at this point. And so we should not be surprised that he has not made a binding commitment to skip the debate. And we should not be surprised to see him at the podium tonight.
In those immortal words: Don’t Panic.