Consider a mechanism that cannot observe how many players there are directly,
but instead must rely on their self-reports to know how many are participating.
Suppose the players can create new identities to report to the auctioneer at
some cost c. The usual mechanism design paradigm is equivalent to implicitly
assuming that c is infinity for all players, while the usual Sybil attacks
literature is that it is zero or finite for one player (the attacker) and
infinity for everyone else (the 'honest' players). The false-name proof
literature largely assumes the cost to be 0. We consider a model with variable
costs that unifies these disparate streams.
A paradigmatic normal form game can be extended into a Sybil game by having
the action space by the product of the feasible set of identities to create
action where each player chooses how many players to present as in the game and
their actions in the original normal form game. A mechanism is (dominant)
false-name proof if it is (dominant) incentive-compatible for all the players
to self-report as at most one identity. We study mechanisms proposed in the
literature motivated by settings where anonymity and self-identification are
the norms, and show conditions under which they are not Sybil-proof. We
characterize a class of dominant Sybil-proof mechanisms for reward sharing and
show that they achieve the efficiency upper bound. We consider the extension
when agents can credibly commit to the strategy of their sybils and show how
this can break mechanisms that would otherwise be false-name proof