ausblenden:
Schlagwörter:
aspiration dynamics; multi-player games; evolutionary dynamics
Zusammenfassung:
On studying strategy update rules in the framework of evolutionary game
theory, one can differentiate between imitation processes and aspirationdriven
dynamics. In the former case, individuals imitate the strategy of a
more successful peer. In the latter case, individuals adjust their strategies
based on a comparison of their pay-offs from the evolutionary game to a
value they aspire, called the level of aspiration. Unlike imitation processes
of pairwise comparison, aspiration-driven updates do not require additional
information about the strategic environment and can thus be interpreted as
being more spontaneous. Recent work has mainly focused on understanding
how aspiration dynamics alter the evolutionary outcome in structured populations.
However, the baseline case for understanding strategy selection is the
well-mixed population case, which is still lacking sufficient understanding.
We explore how aspiration-driven strategy-update dynamics under imperfect
rationality influence the average abundance of a strategy in multi-player evolutionary
games with two strategies. We analytically derive a condition under
which a strategy is more abundant than the other in the weak selection limiting
case. This approach has a long-standing history in evolutionary games
and is mostly applied for its mathematical approachability. Hence, we also
explore strong selection numerically, which shows that our weak selection
condition is a robust predictor of the average abundance of a strategy. The
condition turns out to differ from that of a wide class of imitation dynamics,
as long as the game is not dyadic. Therefore, a strategy favoured under imitation
dynamics can be disfavoured under aspiration dynamics. This does not
require any population structure, and thus highlights the intrinsic difference
between imitation and aspiration dynamics.
