The Traveller's Dilemma

Terry and Jennifer, returning from a remote pacific island, find that the airline has damaged the identical, and ancient idols that each had purchased. An airline manager says he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate the price to defraud the airline.

So the Airline Manager decides to ask each of them to write down the price of the antique as any whole dollar amount between 2 and 100 without conference. Keeping Terry in a small box-like room, and Jenny a similiar closed, windowless room, apart from each other with no possible means of communication between them.

When they are both in their respective rooms the Airline manager decides the following: If both Terry, and Jennifer write the same number - he will take that to be the true price of the strange object and he will pay that amount.

If the two travellers write different amounts, he will assume the lower one is the correct price and the other one is cheating. In that case, he will pay both of them the lower price.

However, he decides that since one of them is cheating he will give them a penalty. He will also reward the other person for being honest. So, the person who wrote the lower number will get 2 more - and the person, who wrote the higher number - will get 2 less than the amount. For instance, if Jennifer writes 46 and Terry writes 100 then Jennifer will get 48 and Terry will 44.

What numbers will Jennifer and Terry write?

And what is the number that you would choose, would it were that you were one of them?