In my design, I have cross-partition transactions, but the way I accomplish this and maintain the Nash equilibrium is I entirely centralized verification, i.e. all transactions are validated by all centralized validators. This eliminates the problem that full nodes have unequal incomes but equal verification costs, thus ameliorates the economics that drives full nodes to become centralized. The centralized validators would still have the potential incentive to lie and short the coin. So the users in the system (hopefully millions of them) are constantly verifying a subsample of the transactions so that statistically a centralized validator is going to get caught fairly quickly, banned, and their hard won reputation entirely blown. Since these validations are done in a non-organized manner (i.e. they are randomly chosen by each node), then there is no viable concept of colluding to maintain a lie.
Regarding the last sentence, I take it that it refers to the extra validation
performed by the users? How do you ensure that the selection of the txs to be validated
is done randomly? And what incentives do the user nodes have to perform the extra validation at all?
Apologies if you have answered these somewhere else, then I'd be grateful
to receive a link.
It seems to me that you are using terms "validation" and "verification"
interchangeably in the above paragraph. (Or does verification refer to the extra
checking performed by the users?)