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Rational Fair Consensus in the GOSSIP Model
The \emph{rational fair consensus problem} can be informally defined as
follows. Consider a network of (selfish) \emph{rational agents}, each of
them initially supporting a \emph{color} chosen from a finite set .
The goal is to design a protocol that leads the network to a stable
monochromatic configuration (i.e. a consensus) such that the probability that
the winning color is is equal to the fraction of the agents that initially
support , for any . Furthermore, this fairness property must
be guaranteed (with high probability) even in presence of any fixed
\emph{coalition} of rational agents that may deviate from the protocol in order
to increase the winning probability of their supported colors. A protocol
having this property, in presence of coalitions of size at most , is said to
be a \emph{whp\,--strong equilibrium}. We investigate, for the first time,
the rational fair consensus problem in the GOSSIP communication model where, at
every round, every agent can actively contact at most one neighbor via a
\emph{pushpull} operation. We provide a randomized GOSSIP protocol that,
starting from any initial color configuration of the complete graph, achieves
rational fair consensus within rounds using messages of
size, w.h.p. More in details, we prove that our protocol is a
whp\,--strong equilibrium for any and, moreover, it
tolerates worst-case permanent faults provided that the number of non-faulty
agents is . As far as we know, our protocol is the first solution
which avoids any all-to-all communication, thus resulting in message
complexity.Comment: Accepted at IPDPS'1
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