There's discussion on the 'necktie paradox' on this blog, where I'm a regular visitor.

I don't agree with the perspectives of those who have responded on that blog.

In the wikipedia, The necktie paradox states that each stands to either win or lose an expensive tie, each at 50% probability, so the game has no advantage to either man.

But, I look at this problem differently:

Say, the cheaper necktie has value y, and
the other one has the value (y + z) with z > 0.

Let's assume that both men have an equal chance of being correct,
the expected value in winnings for either man is,

(0.50)(y + z) – (0.50)(y) = (0.50)z

Both men are expected to make money if they bet.
So both men are correct in choosing to bet.

In the paradox, the essential flaw is calculating relative gain rather than absolute gain. A $100 tie is 10 times more expensive than a $10 tie, but you can't say you expect to gain 900% or lose 90%, since the basis for the two is different. Better to say you stand to gain or lose $90 either way.