An Ambiguous State Machine

We show that a replicated state machine (such as a blockchain protocol) can retain liveness in a strategic setting even while facing substantial ambiguity over certain events. This is implemented by a complementary protocol called "Machine II", which generates a non-ergodic value within chosen intervals such that no limiting frequency can be observed. We show how to implement this machine algorithmically and how it might be applied strategically as a mechanism for "veiling" actions. We demonstrate that welfare-enhancing applications for veiling exist for users belonging to a wide class of ambiguity attitudes, e.g. Binmore (2016), Gul and Pesendorfer (2014). Our approach is illustrated with applications to forking disputes in blockchain oracles and to Constant Function Market Makers, allowing the protocol to retain liveness without exposing their users to sure-loss.