This paper analyzes communication with a language that is vague in the sense that identical messages do not always result in identical interpretations. It is shown that strategic agents frequently add to this vagueness by being intentionally vague, i.e. they deliberately choose less precise messages than they have to among the ones available to them in equilibrium. Having to communicate with a vague language can be welfare enhancing because it mitigates conflict. In equilibria that satisfy a dynamic stability condition intentional vagueness increases with the degree of conflict between sender and receiver.
The paper is discussed in a recent post by Tim Harford:
Alan Greenspan, the mumbling maestro of mixed messages, played the markets with one vague declaration after another, each one a nudge – but not a shove – in the direction he preferred.
The Blume-Board paper lurks on the boundary between philosophy and mathematics – and, ironically, it is extremely precise about what “vagueness” means. A working paper from the economists Florian Ederer, Richard Holden and Margaret Meyer has a more practical bent, examining the boss who finds it useful to be vague about performance bonuses.