'Look, we're not actually willing to cut off our noses to spite our faces, but we want them to believe that we're willing!'
'They'll never believe that, they're not that stupid and they don't think we're that stupid.'
'I think we should actually be prepared to cut off our noses to spite our faces. That'll show em'
'Oh, ok, a person thinks that?'
'Yes, they need our faces to have noses on them more than we need our noses. They need everyone in the room looking beautiful, and we'd ruin that.'
This sort of bizarre logic is what lead the entire world to be pointing nuclear warheads at each other for the last 50 years. As if that's what guaranteed peace in europe, rather than globalisation, greater trading and cultural ties. It's bizarre, and the most prominent example I can think of where individual hoomans may well be bright and clever and sensitive, but get us in a group, and we're rather just a little slow.
If you want a mathematical representation of why this is stupid, look at the
travellers' dilemma.