Blackmail exists when you threaten (explicitly or implicitly) to take a course of action that harms another agent unless that agent takes an action which benefits you. The credibility of your precommitments is not relevant to whether or not an action is blackmail, although it is a factor in how effective your blackmail is.
That the blackmail threat is typically an action which harms the blackmailer is a red herring.
What does “an action that harms another agent” mean? For instance, if I threaten to not give you a chicken unless you give me $5, does “I don’t give you a chicken” count as “a course of action that harms another agent”? Or does it have to be an active course, rather than act of omission?
Is it still blackmail if it’s “justified”? For instance, if you steal me car, and I threaten to call the police if you don’t give it back, is that blackmail?
What does “an action that harms another agent” mean? For instance, if I threaten to not give you a chicken unless you give me $5, does “I don’t give you a chicken” count as “a course of action that harms another agent”? Or does it have to be an active course, rather than act of omission?
It’s not blackmail unless, given that I don’t give you $5, you would be worse of, CDT-wise, not giving me the chicken than giving me the chicken. Which is to say, you really want to give me the chicken but you’re threatening to withhold it because you think you can make $5 out of it. If I were a Don’t-give-$5-bot, or just broke, you would have no reason to threaten to withhold the chicken. If you don’t want to give me the chicken, but are willing to do so if I give you $5, that’s just normal trade.
Harming the blackmailer is simply a proxy for “this isn’t a course of action the blackmailer would otherwise engage in; they do it only for its blackmail effect”
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.
Blackmail exists when you threaten (explicitly or implicitly) to take a course of action that harms another agent unless that agent takes an action which benefits you. The credibility of your precommitments is not relevant to whether or not an action is blackmail, although it is a factor in how effective your blackmail is.
That the blackmail threat is typically an action which harms the blackmailer is a red herring.
What does “an action that harms another agent” mean? For instance, if I threaten to not give you a chicken unless you give me $5, does “I don’t give you a chicken” count as “a course of action that harms another agent”? Or does it have to be an active course, rather than act of omission?
Is it still blackmail if it’s “justified”? For instance, if you steal me car, and I threaten to call the police if you don’t give it back, is that blackmail?
It’s not blackmail unless, given that I don’t give you $5, you would be worse of, CDT-wise, not giving me the chicken than giving me the chicken. Which is to say, you really want to give me the chicken but you’re threatening to withhold it because you think you can make $5 out of it. If I were a Don’t-give-$5-bot, or just broke, you would have no reason to threaten to withhold the chicken. If you don’t want to give me the chicken, but are willing to do so if I give you $5, that’s just normal trade.
Harming the blackmailer is simply a proxy for “this isn’t a course of action the blackmailer would otherwise engage in; they do it only for its blackmail effect”
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.