Any Game Theory Geeks Wanna Take a Crack at This?

[pezzonovante]

This is the classic Ultimatum game.

Two players, A and B.

1. A receives $100.
2. A offers B some sum of money from his pot of $100.
3. B is given two options: Accept the offer from A, in which case A keeps the leftover money, or Reject the offer, in which case A must return all the money to the experiment runner.

It turns out that, at least in the US, people start to choose the reject option quite often if you offer less than $25.  I've seen studies in Europe suggesting that the threshhold is slightly lower there (about $10 to $15 if I remember correctly).

A modified version of the of the Ultimatum Game is as follows:

1. Person A receives a sum of money, either $100 of $500.  Person B is aware that A has received one of the two amounts, but is not told which.   
2. A makes an offer of a sum of money to person B.  A may make the claim that s/he has received the $100 amount regardless of the truth of the statement.
3. B is offered three options:

• Accept the offer per the usual Ultimatum game design,
• Reject the offer per the usual Ultimatum Game design, or
• Pay a third party to find out whether A received the $100 or $500 amount, then choose to Accept of Reject based on this new information.

What extra information do you get by having the underlined rule?  What if the rule were "A cannot make any statement suggestive of which amount s/he received"?