Digging into Plasma talks, I see that that Plasma chains can make periodic commitments to the root chain. Assuming only a single tree depth with users paying validators a fee per transaction, would it be the validators who pay the gas costs for the root commitments by calling a function in the Plasma contract on the root chain? I can't see any other possibility now as contracts cannot pay to execute contracts (yet).
- Periodic updates: indeed, validators are the ones paying the fees (gas) to update the state on the root chain. However, as they are staking funds in the Plasma chain, they collect the fees for transactions and computations performed inside the child chain. Economic incentives ensure the liveness of this ecosystem.
- Exits and fraud proofs: given Byzantine validators, i.e. block withholding attacks, users can exit the Plasma chain using fraud proofs. That is, they possess a merkleised commitment of funds ownership and they publish it on the main chain to challenge malicious contenders. In this scenario, they are forced to pay the gas fee for processing the Ethereum transaction.
Note: regarding 2, there are also the other cases where users may simply want to exit the Plasma chain for personal reasons. It was easier though to highlight a concise example when they need to pay gas.