I would say that if Baron truthfully tells Countess “I have been offered $100,000 for your letters by the Daily Tabloid, but in honor of our friendship I will give you the chance (which I hope you reject) to purchase them instead for only $50,000”, I think this still counts as blackmail, as a matter of ordinary usage. So I agree with Decius in this respect.
For game-theoretic purposes, however, it might be worthy to restrict the definition the way you do, since it calls for a different response strategy: If Baronet also has letters incriminating Countess, but unlike Baron he has to pay to publish them instead of being paid, then it makes sense for Countess to credibly precommit to rejecting any offers from Baronet, but not from Baron.
If the cost to Baron to publish the letters is X, and the blackmail payment is Y, precommit to reject any offers with probability greater than 1-(x/y). That shifts Baron’s expected value to negative (unless x=0), and increases the expected value for Countess by less than (1-(x/y))*(z-y), where z is the loss of value to Countess of having the letters published.
That strategy deters every Baron who is sophisticated enough to be deterred by a full precommittment, and does better against Barons who proceed regardless.
I would say that if Baron truthfully tells Countess “I have been offered $100,000 for your letters by the Daily Tabloid, but in honor of our friendship I will give you the chance (which I hope you reject) to purchase them instead for only $50,000”, I think this still counts as blackmail, as a matter of ordinary usage. So I agree with Decius in this respect.
For game-theoretic purposes, however, it might be worthy to restrict the definition the way you do, since it calls for a different response strategy: If Baronet also has letters incriminating Countess, but unlike Baron he has to pay to publish them instead of being paid, then it makes sense for Countess to credibly precommit to rejecting any offers from Baronet, but not from Baron.
If the cost to Baron to publish the letters is X, and the blackmail payment is Y, precommit to reject any offers with probability greater than 1-(x/y). That shifts Baron’s expected value to negative (unless x=0), and increases the expected value for Countess by less than (1-(x/y))*(z-y), where z is the loss of value to Countess of having the letters published.
That strategy deters every Baron who is sophisticated enough to be deterred by a full precommittment, and does better against Barons who proceed regardless.