A Game Theory Puzzle

A game theory puzzle from an interesting new blog I found:

"On a game show, two people are assigned whole, positive numbers. Secretly each is told his number and that the two numbers are consecutive. The point of the game is to guess the other number.

Here are the rules of the game:

–The two sit in a room which has a clock that strikes every minute on the minute

–The players cannot communicate in any way

–The two wait in the room until someone knows the other person’s number. At that point, the person waits until the next strike of the clock and can announce the numbers

–The game continues indefinitely until someone makes a guess

–The contestants win $1 million if correct, and nothing if they are wrong

Can they win this game? If so, how?"

The solution is a very interesting application of game theory. The solution can be found here.