what if the blackmail is being used against a whole group, not just against one person?
If the group is made up of UDT agents, then they clearly coordinate. If CDT agents are a small fraction of the group (assuming that transaction costs make perfect bargaining non-feasible for CDT agents, as usual), then UDT agents’ (meta)-incentive to reject blackmail will be muted to some degree, depending on the fraction of CDT agents. The opposite consideration applies to the blackmailer’s side: when faced with rejection, she has to expend resources on a costly punishment that will only affect the fraction of agents that’s CDT. So her incentive to engage in blackmail in the first place rises as the fraction of UDT agents drops.
On a different note, assuming that the informational environment is favorable, the best response to “group blackmail” is probably not for each agent to reject blackmail individually, but for all agents to coordinate on incenting whomever can reject blackmail at lowest cost. Under this assumption, UDT agents will have an (meta-)incentive to incent rejection by any agents in their group, including CDT agents. But still, the main result is unchanged; as the fraction of UDT agents falls, the resources expended in providing such incentives will drop proportionally.
If the group is made up of UDT agents, then they clearly coordinate. If CDT agents are a small fraction of the group (assuming that transaction costs make perfect bargaining non-feasible for CDT agents, as usual), then UDT agents’ (meta)-incentive to reject blackmail will be muted to some degree, depending on the fraction of CDT agents. The opposite consideration applies to the blackmailer’s side: when faced with rejection, she has to expend resources on a costly punishment that will only affect the fraction of agents that’s CDT. So her incentive to engage in blackmail in the first place rises as the fraction of UDT agents drops.
On a different note, assuming that the informational environment is favorable, the best response to “group blackmail” is probably not for each agent to reject blackmail individually, but for all agents to coordinate on incenting whomever can reject blackmail at lowest cost. Under this assumption, UDT agents will have an (meta-)incentive to incent rejection by any agents in their group, including CDT agents. But still, the main result is unchanged; as the fraction of UDT agents falls, the resources expended in providing such incentives will drop proportionally.