  The Price of Anarchy (PoA) is a well-established game-theoretic concept to
shed light on coordination issues arising in open distributed systems. Leaving
agents to selfishly optimize comes with the risk of ending up in sub-optimal
states (in terms of performance and/or costs), compared to a centralized system
design. However, the PoA relies on strong assumptions about agents' rationality
(e.g., resources and information) and interactions, whereas in many distributed
systems agents interact locally with bounded resources. They do so repeatedly
over time (in contrast to "one-shot games"), and their strategies may evolve.
Using a more realistic evolutionary game model, this paper introduces a
realized evolutionary Price of Anarchy (ePoA). The ePoA allows an exploration
of equilibrium selection in dynamic distributed systems with multiple
equilibria, based on local interactions of simple memoryless agents.
Considering a fundamental game related to virus propagation on networks, we
present analytical bounds on the ePoA in basic network topologies and for
different strategy update dynamics. In particular, deriving stationary
distributions of the stochastic evolutionary process, we find that the Nash
equilibria are not always the most abundant states, and that different
processes can feature significant off-equilibrium behavior, leading to a
significantly higher ePoA compared to the PoA studied traditionally in the
literature.
