Why the Nash Bargaining Solution will probably mean heartache for the U.S. tomorrow: Those who have seen the Oscar-winning film A Beautiful Mind probably remember the bar scene, where John Nash and some buddies spot a gorgeous blonde and several brunettes walk into a bar. His buddies, naturally, want to go after the blonde, presuming that even if they fail, one of the attractive but not stunning brunettes (Jennifer Connelly shows up later) will be there as a consolation prize. Nash, however, realizes that the best strategem would be to ignore the blonde, and pursue the more-attainable brunettes: all of them going after the same woman, even if she is the most desirable, would only offend her friends, harming the ability for all of them to get a lil sompn' sompn', while not assuring that even the least geeky of the lot would get lucky with the blonde.

It's a little bit more complicated than that, movies generally having to focus on a core audience beyond Ivy League mathematicians, but it does explain why the U.S. has its work cut out for it tomorrow if it wants to advance to the second round of the World Cup. On paper, it's simple: the U.S. has to beat Ghana by four goals. That gets Team U.S.A. in, no matter what else happens. Since that is highly unlikely, the Americans not having scored four goals in a game for some time, and Ghana having just manhandled the same team that beat the U.S., 3-0, in the opener, the next best scenario is for the U.S. to beat Ghana, and Italy to beat the Czech Republic.

Even if the first thing happens, I think it's unlikely the second will. Italy has very little incentive to win tomorrow, and neither, for that matter, does the Czech Republic. The optimum result for both teams would be a tie, since both could advance. In fact, Italy would definitely advance, and the Czechs would in almost every other scenario; only a Ghana victory would knock them out. Similarly, a 1-0 loss to the Czechs would also likely assure both teams of advancing in almost every scenario. The U.S. would either have to blow out Ghana, or Ghana would have to win; a tie or close U.S. win sends both forward. Both teams can watch the scoreboard, and if Ghana strikes first, they can react accordingly, but if it appears that our game is a taut, close affair, there's no incentive to open things up.

There is one obvious benefit to winning the game: avoiding a second round matchup with Brazil. But Italy wins the group with a tie, unless, of course, Ghana wins. However, an Italian victory knocks out the Czechs, while a decisive Czech victory would almost certainly eliminate the Italians. A safe, defensive battle would likely help both teams, while a wide-open, offensive match would kill the loser. And if there is anything the Azzurri does really, really well, its play dull, tactical, defensive soccer. So it looks like we'll have to wait til 2010....