A multi-prover interactive proof protocol, as described here, consists of computationally unbound provers $P_1,P_2,\ldots$ which together convince a polynomial-time verifier $V$ of some proposition, under the assumption that the provers can't communicate after some initial setup. Are there practical scenarios in which such a protocol would be useful?
The linked paper gives an example of a user inserting two bank cards into an ATM to prove their identity. I'm skeptical of this use case because:
- It would be difficult to physically ensure fraudulent cards are unable to communicate.
- Single-prover protocols (possibly relying on cryptographic assumptions) have been sufficient for this use case so far.
- The bank cards are not computationally unbounded; presumably the ATM has at least as much computational power as the cards, and could just run the honest verifier algorithm itself.
Note: Point 3 would not apply if, rather than computationally unbound provers, we considered polynomial-time provers with access to a secret. Has that class of protocols been studied?
Note: The study of this class of decision problems may have theoretical value (example) but I'm not asking about that.