Evolutionary game theory is used to model the evolution of competing strategies in a
population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in
which any competing mutated strategy would be wiped out from a population. If a strategy
is weak evolutionarily stable, the competing strategy may manage to survive within the
network. Understanding the network-related factors that affect the evolutionary stability
of a strategy would be critical in making accurate predictions about the behaviour of a
strategy in a real-world strategic decision making environment. In this work, we evaluate
the effect of network topology on the evolutionary stability of a strategy. We focus on two
well-known strategies known as the Zero-determinant strategy and the Pavlov strategy.
Zero-determinant strategies have been shown to be evolutionarily unstable in a well-mixed
population of players. We identify that the Zero-determinant strategy may survive, and
may even dominate in a population of players connected through a non-homogeneous
network. We introduce the concept of ‘topological stability’ to denote this phenomenon.
We argue that not only the network topology, but also the evolutionary process applied and
the initial distribution of strategies are critical in determining the evolutionary stability of
strategies. Further, we observe that topological stability could affect other well-known
strategies as well, such as the general cooperator strategy and the cooperator strategy.
Our observations suggest that the variation of evolutionary stability due to topological
stability of strategies may be more prevalent in the social context of strategic evolution,
in comparison to the biological context.
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