  We propose a novel distributed monetary system called Hearsay that tolerates
both Byzantine and rational behavior without the need for agents to reach
consensus on executed transactions. Recent work [5, 10, 15] has shown that
distributed monetary systems do not require consensus and can operate using a
broadcast primitive with weaker guarantees, such as reliable broadcast.
However, these protocols assume that some number of agents may be Byzantine and
the remaining agents are perfectly correct. For the application of a monetary
system in which the agents are real people with economic interests, the
assumption that agents are perfectly correct may be too strong. We expand upon
this line of thought by weakening the assumption of correctness and instead
adopting a fault tolerance model which allows up to $t < \frac{N}{3}$ agents to
be Byzantine and the remaining agents to be rational. A rational agent is one
which will deviate from the protocol if it is in their own best interest. Under
this fault tolerance model, Hearsay implements a monetary system in which all
rational agents achieve agreement on executed transactions. Moreover, Hearsay
requires only a single broadcast per transaction. In order to incentivize
rational agents to behave correctly in Hearsay, agents are rewarded with
transaction fees for participation in the protocol and punished for noticeable
deviations from the protocol. Additionally, Hearsay uses a novel broadcast
primitive called Rational Reliable Broadcast to ensure that agents can
broadcast messages under Hearsay's fault tolerance model. Rational Reliable
Broadcast achieves equivalent guarantees to Byzantine Reliable Broadcast [7]
but can tolerate the presence of rational agents. To show this, we prove that
following the Rational Reliable Broadcast protocol constitutes a Nash
equilibrium between rational agents and may therefore be of independent
interest.
