  Modern blockchains guarantee that submitted transactions will be included
eventually; a property formally known as liveness. But financial activity
requires transactions to be included in a timely manner. Unfortunately,
classical liveness is not strong enough to guarantee this, particularly in the
presence of a motivated adversary who benefits from censoring transactions. We
define censorship resistance as the amount it would cost the adversary to
censor a transaction for a fixed interval of time as a function of the
associated tip. This definition has two advantages, first it captures the fact
that transactions with a higher miner tip can be more costly to censor, and
therefore are more likely to swiftly make their way onto the chain. Second, it
applies to a finite time window, so it can be used to assess whether a
blockchain is capable of hosting financial activity that relies on timely
inclusion.
  We apply this definition in the context of auctions. Auctions are a building
block for many financial applications, and censoring competing bids offers an
easy-to-model motivation for our adversary. Traditional proof-of-stake
blockchains have poor enough censorship resistance that it is difficult to
retain the integrity of an auction when bids can only be submitted in a single
block. As the number of bidders $n$ in a single block auction increases, the
probability that the winner is not the adversary, and the economic efficiency
of the auction, both decrease faster than $1/n$. Running the auction over
multiple blocks, each with a different proposer, alleviates the problem only if
the number of blocks grows faster than the number of bidders. We argue that
blockchains with more than one concurrent proposer have can have strong
censorship resistance. We achieve this by setting up a prisoner's dilemma among
the proposers using conditional tips.

Theoretical Economics;Computer Science and Game Theory