Use monetary rewards (or penalties) if need be. Here is Joshua Gans applying some game theory to the vaccine passport idea:
Vaccine hesitancy is modelled as an endogenous decision within a behavioural SIR model with endogenous agent activity. It is shown that policy interventions that directly target costs associated with vaccine adoption may counter vaccine hesitancy while those that manipulate the utility of unvaccinated agents will either lead to the same or lower rates of vaccine adoption. This latter effect arises with vaccine passports whose effects are mitigated in equilibrium by reductions in viral/disease prevalence that themselves reduce the demand for vaccination.
A “utility tax” is rarely a good idea. Besides what happens if you lose your smart phone? Don’t have one to begin with? Arrive from another country with an incompatible information/verification system?
With cases falling in both the UK and Netherlands, the vaccine passport idea, at the governmental level, is looking worse and worse. That said, I am all for private entities making their own decisions on these issues, and generally I am happy when I see employers require vaccination.
Addendum: Here is a Gans tweet storm on the paper.